
Class -UxxU^^lL 



(x)[PglitN»__L9_La 



OJ- 



THE OVERLAPPING OF ATTAINMENTS IN 

CERTAIN SIXTH, SEVENTH, AND 

EIGHTH GRADES 



' BY 

PAUL J. KRUSE, Ph.D. 



TEACHERS COLLEGE, COLUMBIA UNIVERSITY 
CONTRIBUTIONS TO' EDUCATION, No. 92 



PUBLISHED BY 

^eacf)er£( College. Columbia ®nibersiitp 

NEW YORK CITY 
1918 

iHonograpUii. 



,^i\ 



^'^Kl 



\^\l'>' 



Copyright, 1918 
By Paul J. Kruse 



FEB 24 lt^l9 



THE HERSHEY PRESS. HERSHEY. PA. 



>CI.Ar)|5332 



'MO ( 



ACKNOWLEDGMENTS 
It is only through the co-operation of those interested in the 
promotion of the science of education that studies of this nature 
are possible. I am glad to acknowledge my indebtedness and 
record my thanks to those teachers in the Seattle Pubhc Schools 
whose inteUigent co-operation made the giving of the tests far 
less difficult than it would otherwise have been. To the genuine 
professional interest and ever courteous help of Supt. F. E. Wil- 
lard and Principals A. S. Gist, W. H. EUert, R. W. Moore and 
Charles W. Metsker I owe much. I am unable to express even a 
small part of my great obhgation and deep gratitude to Professor 
E. L. Thorndike for his helpful aclvice and encouragement through- 
out this investigation, and for his generous giving of valuable 
time and help on other occasions. Without the encouraging 
assistance given by my wife through the months of testing, scor- 
ing, and calculating, the completion of the study at this time 
would have been impossible. P J K 



CONTENTS 

Chapter P^ge 

I Introduction 5 

1 Evidences of Overlapping 

2 The Problems 

II The Data 3 

1 The Subjects 

2 Tests Used 

3 Administration of the Tests 

4 Scoring the Tests 

III Overlapping by Single Tests 30 

1 The Measure of Overlapping 

2 Elimination of Some Tests 

3 Comparison of Different Tests as to Amount of Overlapping 

4 Surfaces of Overlapping 

IV Overlapping in the Case of Composites 42 

1 Results 

2 Surfaces of Overlapping 

3 Statistical Treatment 

V Reliability of the Tests Used as Determined by the Cor- 
relation OF Groups of Similar Tests 57 

VI Comparison of Results in Overlapping With Those of 

Other Investigators 59 

VII Conclusions 67 

VIII Bibliography 69 

IX Appendix 71 



THE OVERLAPPING OF ATTAINMENTS IN CERTAIN 
SIXTH, SEVENTH, AND EIGHTH GRADES 

I 

INTRODUCTION 

1. Evidences of Overlapping 

One of the most important findings resulting from the measure- 
ment of the achievements of pupils by means of standard tests is 
the great variabiUty in a given grade. This brings in question 
our whole system of grading, which proceeds upon the assump- 
tion that we have in a given grade pupils differing markedly in 
ability to do the work of the school from those in the grades 
above and below. There is a tacit understanding that the pres- 
ence of a pupil in the seventh grade, for example, means that his 
ability is greater than that representative of the sixth grade and 
less than that of the eighth grade. The results of much of the 
testing taken at face value seem to challenge very seriously the 
validity of these assumptions. 

Some of the findings of the Butte Survey Commission are in- 
dicated in the following extracts. (14) 

"A very wide range of ability in each grade is revealed (in com- 
position) . . . One eighth-grade pupil wrote a composition 
rated while two pupils wrote papers rated 7 on the scale of 10. 
The eighth-grade group range rather evenly over aU the steps of 
the scale from 1 to 6 ... We see that some fourth-grade 
pupils surpass the median ability of the eighth-grade pupils, 
while many eighth-grade pupils fall below the median ability of 
the fourth-grade pupils." (p. 74) "As in spelling and composi- 
tion, a very wide range of abifities in penmanship is found in each 
grade .... Some children in the second grade surpass 
the abiUty of the median eighth-grade pupil, while some in the 
eighth grade fall below the median second-grade pupil." (p. 81) 

5 



6 The Overlapping of Attainments in Certain Grades 

Dr. Daniel Starch in his "Educational Measurements" (16) 
makes repeated reference to this overlapping of grades. "There 
are pupils in the fourth grade whose attainment in reading is 
higher than that of the average eighth-grade pupil. Likewise, 
there are pupils in the fourth grade whose attainment in reading 
is inferior to that of the average first-grade pupil." (p. 40) "In 
speed and comprehension combined, 31.8 per cent of the pupils 
of any grade reached or exceeded the median of the next grade 
above, 20.1 per cent reached or exceeded the median of the second 
grade above, 13.2 per cent reached or exceeded the median of the 
third grade above, and 3.3 per cent reached or exceeded the median 
of the fourth grade above." (p. 42) "We find that in quaUty of 
writing on the average 37.1 per cent of the pupils of any given 
grade reach or exceed the median of the next grade above it, 24.0 
per cent reach or exceed the median of the second grade above it, 
14.6 per cent reach or exceed the median of the third grade above 
it, and 7.7 per cent reach or exceed the median of the fourth grade 
above it. Statements of the same sort apply to the speed of 
writing." (pp. 86, 88) "The spelling tests reveal identically the 
same facts concerning the distribution of the pupils and the over- 
lapping of the grades as were found in case of the reading and 

writing tests The overlapping among the various 

grades is enormous. There are two pupils in the second grade 
who can spell as well as two pupils in the eighth grade . . . 
On the average 20.8 per cent of the pupils of any grade reach or 
exceed the median of the next grade above it, and 6.2 per cent 
reach or exceed the median of the second grade above it." (p. 98) 

2. The Problems 
These statements suggest many questions the answers to which 
should be highly significant for educational theory and school 
practice. 

a. Will further investigation under carefully controlled condi- 
tions support these findings? 
6. Have we in the results from single tests in different traits 
a valid measure of the overlapping of general ability to do 
the work of a given grade? 
c. Is our grading system, in which we have had so much 
faith, really as bad as it appears to be as a means of select- 
ing on the basis of achievement? 



Introduction 7 

d. There is a tacit feeling that the passing from one grade to 
the next — with all the tribulation which it entails on the 
part of pupil and teacher — means a very definite step 
in accompUshment. Is this feeling well founded? 

€. What constitutes a valid measure of overlapping? 

It was in the hope of presenting some facts that would have a 
direct bearing on these and similar questions that this study was 
undertaken. 

Primary Problem. To determine from data, adequate and re- 
liable, the amount and nature of the overlapping in certain sixth, 
seventh, and eighth grades. 

Related Problem. To get a measure of the reliability of certain 
tests as measures of attainment by school pupils in these grades. 



II 

THE DATA 

It was recognized at the beginning that whatever value might 
come from such a study as the one contemplated would depend 
very laigely upon (a) the number of pupils tested, (6) the number 
and worth of the tests used, (c) the uniformity of procedure in 
giving the tests, (d) the opportunity given the pupils to show their 
real capacity in each test, (e) the consistency in the scoring of the 
papers. 

1. The Subjects 

The pupils tested were all the sixth-, seventh-, and eighth- 
grade pupils in four pubhc schools in Seattle, Washington. About 
860 pupils in aU were tested, this being the number represented 
in the final composite: 254 in the sixth grade, 324 in the seventh, 
and 282 in the eighth. The discrepancy between these figures 
and the totals for certain tests is accounted for by the fact that 
missing scores for a certain minimum number of tests were inter- 
polated in making the composites, by a method that will be ex- 
plained in a later section. 

The schools were chosen so as to represent different types as to 
size and sociological conditions of environment. School No. 1 
is a small, comparatively new school in the outskirts of the city, 
drawing some pupils from less well-graded districts. The com- 
munity is largely composed of people of the artisan classes. School 
No. 2 is also a small school, but in an old and rather unprogressive 
section of the city. No. 3 is a large cosmopolitan school with 
a varied school population. No. 4 is also a large school and is 
in one of the best residence sections of the city largely composed 
of business and professional classes. 

Table I shows the distribution of classes by schools, rooms, and 
grades. 



The Data 







TABLE 1 










Distribution of 


Classes by Schools, Rooms, 


AND 


Grades 






No. 












School 


of 




Number of Classes 








Rooms 


Grade VI 


Grade VII 


Grade VIII 


Total 


No. 1 . . 


5 


2 


3 




2 


7 


No. 2.. 


4 


2 


3 




2 


7 


No. 3.. 


7 


3 


3 




2 


8 


No. 4.. 


8 


3 


3 




3 


9 


All 


24 


10 


12 




9 


31 



2. Tests Used 

The tests used were: 

Addition, Woody Scale, Series A 

Subtraction, W oody Scale, Series A 

Multiplication, Woody Scale, Series A 

Division, Woody Scale, Series A 

Problems I 

Problems II 

Problems III 

Trabue Completion-Test Language Scale B 

Trabue Completion-Test Language Scale C 

Trabue Completion-Test Language Scale D 

Trabue Completion-Test Language Scale E 

Composition I. A Letter ApplyingJor a Job. 

Composition II. On the topic, "The Study I Like Best and Why, and the 
Study I Like Least and Why." 

Paragraph Reading, Thorndike Reading Scale Alpha 2 

SpeUing, last 20 words in column "U" of Ayres' Measuring Scale for Abil- 
ity in Spelling 

Opposites, Al 

Opposites, A2 

Opposites, A3 

Opposites, A4 

Whole-Part, Bl 

Adjective-Substantive, B2 

Verb-Object, CI 

Species-Genus, C2 

Part-Whole, C3 

Mixed Relations, Dl 

Mixed Relations, D2 

Directions. X 

Directions, VI 

Directions, VII 

Visual Vocabulary, VIII 

Visual Vocabulary, XIII 



10 



The Overlapping of Attainments in Certain Grades 



Specific references to the sources of those tests which are readily 
available are given in the appended bibliography, as follows: 
Woody Arithmetic Scales (27) 
Trabue Language Scales (25) 
Thorndike Reading Scale Alpha 2 (20) 
Ayres' Measuring Scale for Ability in SpeUing (1) 
Directions, X (24) 
Directions, VI (24) 

The other tests are reproduced below.^ 



Write your name here Write your age here . . years . . months. 

Write the date here 

Write after each word on this page its opposite as shown in the first five. 
If you do not know the opposite of a word go on to the next word. 

good — bad 

day — night 

up — down 

friend — enemy 

true— false 

high 

summer 

long 

soft 

white 

far 

up 

smooth 

lost 

wet 

high 

dirty 



day 

yes 

wrong 

empty 

top 

north 

sour 

out 

weak 

good 



after 

above 

sick 

slow 

large 

rich 

dark 

front 

love . 

taU 

open 

summer 

new 

come 

male 

to reveal 

level 

past 

common 

foreign 

sane 

country 

rapid 



^The writer is indebted to Professor Thorndike for these tests. 



The Data 



11 



A-2. 



Write your name here Write your age here, .years, .months. 

Write the date here 

Write after each word on this page its opposite as shown in the first five. 
If you do not know the opposite of a word go on to the next word. 

good — had 

day — night 

up — down 

friend — enemy 

true— false 

early extravagant 

dead obscure 

hot opaque 

convex 

heterodox 

collect 

prompt 

strong 

to lead 

courteous 

tragic 

diminish 

erroneous 

fact 

jtale 

genuine 

broken 

permit 

descend 

expensive 

divine 

all 

from 



serious 

grand 

to win 

to respect 

clean 

few 

alike 

deep 

hiss 

encourage 

coarse 

melt 

double 

dwarf 

plural 

valley 

to benefit 

future 



A-3. 



Write your name here Write your age here . . years . . months. 

Write the date here 

Write after each word on this page its opposite as shown in the first five. 
If you do not know the opposite of a word go on to the next word. 



good — bad 
day — night 
up — down 
friend — enemy 
true— false 



12 



The Overlapping of Attainments in Certain Grades 



frequently 

to lack 

apart 

stormy 

motion 

forcible 

straight 

to hold 

loquacious 

forbid 

sdways 

grief 

sickly 

negative 

soothing 

free 

superior 

separate 



city 

attractive 
stupid 
shallow 



savage 

different 

to marry 

every 

mascuhne 

obnoxious 

enlarge 

joy 

scowl 

sacred 

inhale 

aristocratic 

help 

foolish 

pay 
wild 

precise 

dwindle 

drunk 

fluctuating 

first 

horizontal 



A-4. 



Write your name here Write your age here . . years . . months. 

Write the date here 

Write after each word on this page its opposite as shown in the first five. 
If you do not know the opposite of a word go on to the next word. 



good — bad 

day — night 

up — down 

friend — enemy 

true — -false 

after 

to float 

rough 

to bless 

to take 

exciting 

clumsy 

unless 

tender 

public 

raise 



remember 

increase 

preserve 

debit 

if 

vertical 

ignorant 

rude 

simple 

deceitful 

stingy 



The Data 



13 



impoverish 

cruel 

generous 

ancient 

silly 

multiply 

desist 

survive 

proficient 

hindrance 

strength 

innocent 



permanent 

over 

to degrade 

weary 

to spend 

part 

together 

gradual 

victorious 

optimist 

laugh 

numerous 



B-1. 



B-2. 



Write your name here Write your name here 

Write your age here . . years . . months Write your age here . . years . . months 

Write the date here Write the date here 

Write words that fit the Write words that fit the 

words in this column in the words in this column in the 

way shown in the first three. way shown in the first three. 



face — nose 

tree — branch 

store — counter 

apple 

clock 

knife 

book 

hat 

pencil 

hand 

dog 

oyster 

church 

chair 

bird 

banana 

shoe 

train 

finger 

house 

coat 

cart 

face 



wet — water 

ted — rose 

sharp — knife 

sharp 

hot 

dusty 

raw 

deep 

ripe 

funny 

tall 

stormy 

new 

hiUy 

strong 

muddy 

pretty 

noisy 

white 

steep 

round 

smoky 

curly 



11 The Overlapping of Attainments in Certain Grades 

C-1. 

Write your name here Write your age here . . years . . months. 

Write the date here 

After each word printed below you are to write some word, according to 
the further directions. Write plainly. If you cannot think of the right 
word, go ahead to the next. 

Write words that fit the words in this column, 
in the way shown in the first three. 

drink — water 
ask — questions 
subtract — numbers 

bake light 

spill sail 

kiss spin 

polish lock 

sweep wash 

fill pump 

sharpen learn 

write open 

chew eat 

drive climb 

read lend 

tear smoke 

throw singe 

paint dig 

mail sift 

C-2. 

Write your name here Write your age here, .years, .months. 

Write the date here 

After each word printed below you are to write some word, according to 
the further directions. Write plainly. If you cannot think of the right 
word, go ahead io the next. 

Write words that tell what sort of a thing each 
thing named is, as shown in the first three. 

lily — flower 
blue — color 
diamond— jewel 

penny iron 

dictionary green 

cabbage 42 

Rhine parlor 

murder ruby 

dog orange 



The Data 15 



sparrow cat 

London September 

foot-ball dime 

rose elm 

diphtheria France 

robin skirt 

Pacific a rattle 

cod Christmas 

baseball muslin 



C-3. 

Write your name here Write your age here . . years . . months. 

Write the date here 

After each word printed below you are to write some word, according to 
the further directions. Write plainly. If you cannot think of the right 
word, go ahead to the next. 

Write words that fit the words in this column, 
in the way shown in the first three. 

sleeve — coat 
nose— face 
roof — house 

elbow sleeve 

hinge brick 

page deck 

finger France 

wing pint 

morning fin 

Wade steeple 

mattress month 

chimney hub 

cent chin 



D-1. 

Write your name here Write your age here . . years . . months. 

Write the date here 

Write in each line a fourth word that fits the third word in that line in the 
way ttiat the second word fits the first, as shown in the first three fines. 



color— rerf 


name — John 






page— 600^ 


handle — knife 






fire — burns 


soldiers— fight 






good— bad 


long- 


deep — valley 


high- 


eagle— bird 


shark- 


growls— dog 


roars — 


eat— bread 


drink- 


brick— waU 


page— 



16 The Overlapping of Attainments in Certain Grades 



fruit — orange 
sit — chair 
double — two 
England — London 
chew — teeth 
pen — write 
water — wet 
laborer — works 
come — came 
north — south 
mend — clothes 
lily — flower 
ton — pound 
elbow — arm 
pea — pod 
past — present 
bell — rings 



vegetable- 
sleep — 
triple — 
France — 
smell — 
knife — 
fire — 
soldier — 
go- 
far— 
bake — ■ 
oak — 
pound — 
chin — 
nut — 
present — 
clock — • 



lathe — machine 


hammer— 


pencil — lead 


book- 


high — ^low 


up— 


sheep — lamb 


dog- 


Thursday-Friday 


June — 


build — house 


paint- 


one — single 


two — 


eye — see 


ear — 


Monday-Tuesday April- 


do— did 


see — 


bird— sings 


dog- 


hour — minute 


minute — 


straw— hat 


leather- 


cloud— rain 


sun — 


hammer— tool 


dictionary- 


uncle — aunt 


brother — 


dog— puppy 


cat— 



D-2. 

Write your name here Write your age here . . years . . months. 

Write the date here 

Write in each line a fourth word that fits the third word in that line in the 
way that the second word fits the first, as shown in the first three lines. 



color — red 


name — John 






page — book 


handle — knife 






fire — burns 


soldiers— fight 






he — him 


she — 


dusty — dry 


muddy — 


boat — water 


train — 


floats— raft 


sails — 


crawl — snake 


swim — 


deck — ship 


mattress — 


horse— colt 


cow — 


iron — metal 


Latin- 


nose — face 


toe- 


cat — kitten 


hen— 


bad— worse 


good- 


dark— fight 


hot— 


hungry— food 


thirsty- 


month-December 


hoUday 


hat— head 


glove— 


spin — top 


sheupen — 


ship — captain 


army— 


second — minute 


minute — 


man — woman 


boy- 


pencil— lead 


book- 


axe — cuts 


pin— 


Uttle— less 


much — 


yard — foot 


foot- 


wash — face 


sweep— 


early — late 


new — 


house — room 


book- 


shoot — gun 


smoke — 


sky — blue 


grass— 


Atlantic— ocean 


Mississippi — 


swim — water 


fly- 


has— had 


is — 


once — one 


twice — 


month— year 


day — 


cat— fur 


bird- 


my — mine 


they— 


pan— tin 


table— 


room — ceiUng 


house- 


buy— sell 


come— 


baby — cries 


bird— 


oyster — shell 


banana— 



The Data 17 

VII 

DO WHAT IT SAYS TO DO 

21. Show by a cross which costs most: an orange 

a suit of clothes 
a pair of skates 
a pound of sugar 

22. Show by a cross which tastes best: dirty paper 

coal dust 
roast beef 
sour milk 

23. How many legs has a horse? Write the answer. 

24. How many more legs has a horse than a boyP Write the answer. 

23. Show by a cross which you would like best to own: 
a toy boat 
a gold ring 
a thoussmd dollars 
a sharp knife 

26. Show by a cross which you would enjoy most: 

being hit with a club 
having your shoulder pinched 
receiving a gift of money 
losing many toys * 

27. Show by a cross the word that means pleasant: 

entrance 
entreat 
entangle 
enjoyable 

28. Show by a cross the words that tell something a boy ought to do: 

perform miracles 

overeat habitually 

study his lessons 

strain his eyes 
2\>. Show by a cross which is hardest to do: 

To run a mile in a second 

To stay awake all night 

To pay attention in school 

To play out-doors 
30. Show by a cross the least dangerous thing: 

To sit in front of a trolley car 

To sit in the snow all night 

To play with a loaded gun 

To sit still in front of a mirror 



18 The Overlapping of Attainments in Certain Grades 

31. Show by a cross each word that means unhappy. 

grotesque 

wretched 

sincere 

miserable 

sad 

notable 

sane 

joyless 

grateful 

uncomfortable 

32. Show by a cross each word that means to make clear or something like 

to make clear: 

execrate 

elevate 

elucidate 

traduce 

explain 

clarify 

satisfy 

expound 

extort 

antipathy 

VIII 

Write a letter b under every word that means some part of the body. Write 
a letter t under every word that is the name of a tool. Write a letter s under 
every word that means something to do with the sea or ships. Write a letter 
h under every word that means some part of a house. 

Remember — b, for parts of the body 
t, for tools 

s, for words about the sea and ships 
h, for parts of a house 

arms, ear, wave, door, eye, ship, hall, saw, bone, sail, hammer, wall, ocean, 

face, deck, window, axe, float, mast, chamber, foam, file, canoe, billow, 

cellar, knife, harbor, elbow, coast, attic, brain, bosom, basement, breast, 

laimch, artery, chisel, shin, ceiling, brace, tongue, helm, garret, porch, gulf, 

kitchen, hatchet, fleet, balcony, gimlet, channel, casement, cargo, entry, 

cruise, embark, chimney, thigh, tiller, awl, alcove, ell, keel, piazza, cleaver, 

spine, screw-driver, dormer, bevel, cartilage, rudder, corridor, eaves, ratchet. 



The Data 19 

kidney, hurricane, gable, lathe, cerebellum, lagoon, plane, maUet, leeward, 
hearth, vise, cranium, nauticeJ, wainscot, adze, ligament, cornea, augur, 
navigable, patella, starboard, lymph, mariner, peritoneum, hull, jetty. 

xm 

Look at each word. Think what it means. If it means a color like red 
or blue, write a letter c under it. If it means something about a number, 
like six, all, half, many, write n under it. If it means something about time, 
like now. Me, when, never, write t under it. If it means something about di- 
rection or location, if it is a word like east, north, up, down, above, behind, 
write d under it. 

Remember — c, for words about color, like red, blue, green 

n, for words sibout number, like more, five, many 

t, for words about time, like then, often, early 

d, for words about direction and location, like front, east, here 

last, west, here, half, early, brown, many, below, there, month, across, year, 
noon, back, forty, gray, first, right, pair, left, green, morning, whole, pink, 
while, where, afternoon, minute, gold, edge, soon, outside, some, more, evening, 
plum, inside, beneath, odd, even, every, yellow, monday, toward, dozen, 
June, group, future, buff, from, count, nine, forenoon, purple, middle, plural, 
tuesday, instant, couple, score, crimson, april, each, during, interior, forward, 
Wednesday, never, december, singular, center, hazel, outward, several, sceu-let, 
violet, double, frequent, chestnut, august, ruby, either, rarely, recent, over- 
head, million, tan, exterior, queutet, seldom, tawny, olive, January, margin, 
numerous, immediate, bounding, february, encircling, September, lilac, 
numeral, crowd, gradual, roan, quadruple, opposite, minority, november, 
russet, diagonal, October, faun, formerly, garnet, overhanging, multitudinous, 
lasting, meantime, duplicate, continue, intervening, perpendicular, henceforth, 
elevated, lavender, forthwith, sextet incessant, azure, surmounting, majority, 



20 The Overlapping of Atlainmenis in Certain Grades 

previous, interim, thereabouts, plurality, narrow, perennial, frontal, treble, 
repeatedly, constantly, carmine, neighboring, parallel, contemporary, vertical, 
mauve, decade, emerald, magenta, octile, ecru, contiguous, qxiintet, ensuing, 
horizontal, evanescent, sepia, conterminous, multiple, integer, vermillion, 
eternal, turquoise, transverse, century, sexagesimal, ephemeral. 

Problems — I 
Begin with No. 1 and see if you can solve all ten correctly. 

1. How much change should I expect from $5.00, after paying for 5 
pounds of coffee at 38 cents a pound? 

2. A baseball team played 160 games during the season and won 100 of 
them. What part of the whole number of games did the team win? 

3. If $1,991 a day is paid to 724 men who each earn the same wages, 
how much does each man receive? 

4. The children of a school made badges. Five hundred and fifty were 
needed. In 4 days grades 3 to 7 made 20, 25, 63, 132 and 144 badges. 
The eighth grade agreed to make the rest. How many did the eighth 
grade agree to make? 

5. A man has a salary of $125 a month. He saves 20 per cent of his 
salary. How much will he save in a year? 

6. A store takes in the following sums: $1,250.50, $300, $175, $16.25, 
$120.50, $32.75, $68.50. It pays out: $600, $360, $166.67, $44.33, 
$240. How much remeiins after payments are made? 

7. Mr. Marshall receives a salary of $2500 a year. His rent costs him 
one-fifth of this and his other expenses are $1,500. He saves the 
rest. What per cent of his salary does he save? 

8. A grocer had a tank holding 44% gallons of oil. One day he drew 
out 1534 gallons and the next day 9}i gallons. How many gallons 
were left in the tank? 

9. How much will Mr. Fox receive for 8% dozen pencils at the rate of 6 
for 25c? 

10. John is 4 ft. 9 in. How tall will he be in two years if he grows 3J^ 
per cent of his present height the first year, and 3}^ P^r cent of his 
height a year from now the second year? 

Problems — II 
Find how long Meuy was allowed to play on each of these days. 



The Data 21 

1. Monday. It is 4.10 P. M. Mother says to Mary, "You may play 

till quarter past five " 

2. Tuesday. It is 4.20 P. M. Supper is at 6 o'clock. Mother says, 
"You may play half the time from now till supper time." 

3. Wednesday. It is 4.05 P. M. Mother says, "If you will help me for 
half an hour now, and for 10 minutes before supper you may play the 
rest of the afternoon." 

4. Thursday. Mother says, "You may play 20 minutes and 2}4 minutes 
more for every piece you iron." Mary irons 28 pieces. 

5. Friday. Mother says, "You may play 2 minutes for every 3 problems 
you solve, and .5 minutes more for every problem you solve correctly." 
Mary solved 15 and had all but one right. 

6. Saturday. Mother says, "You may play 2 hours for nothing. Also 
I will allow you 10 minutes for every problem you solve correctly, but 
wiU take off 10 minutes for every problem that is wrong. Also you 
may play IJ^ minutes for every minute you help me by minding your 
little brother." Mary did 10 problems, and had only one of them 
wrong. She minded the baby for an hour and a quarter. 

Problems — III 

See how many of these problems you can do correctly. All the problems 
ask the same question, "How many minutes is it from the time John begins 
to pump until the tank is filled?" The tank holds 120 gallons and is sup- 
posed always to be empty when John begins to work. 

1. John pumps 2 minutes before any water reaches the tank. Then he 

pumps water into it at the rate of 3 gallons a minute until the tank is 
fuU. 

2. John pumps IJ^ min. before any water reaches the tank. Then he 
pumps water into it at the rate of 3 gallons a minute, for 20 min. Then 
he pumps at the rate of 2 gallons a minute until it is fuU. 

3. John pumps 1 min. before any water reaches the tank. Then he 
pumps water into it at the rate of 24 gallons in 10 minutes until the 
tank is full. 

4. John pumps 2 min. before any water reaches the tank. Then he 
pumps for 15 min. at the rate of 3 gallons per minute. Then Dick 
helps him and they pump at the rate of 5 gallons per minute until the 
tank is full. 

5. John pumps 1^ min. before any water reaches the tank. Then he 
pumps for 10 min. at the rate of 2.7 gallons per minute. Then the 
pump breaks and he spends 8 min. mending it. Then he pumps at 
the rate of 3.1 gallons per minute until the tank is fuU. 



22 The Overlapping of Attainments in Certain Grades 

6. John pumps for 1 min. 50 sec. before any water reaches the tank. 
Then he pumps at the rate of 3.6 gallons per minute for 10 min., then 
rests 5 min., then pumps 3.6 gal. per minute for 10 minutes, then rests 
5 min., then pumps 3.6 gal. per min. for 10 minutes, then rests 5 min., 
and so on until the tank is filled. 

The selection of the tests used was made with the following 
aims in mind: 

a. To make as thorough a testing as time would permit. 

b. To have the two general fields of Arithmetic and English 
well represented. 

c. To use the best available tests in school subjects, suited to 
the purpose of this study. 

The Woody Arithmetic Scales furnish a real test for the sixth, 
seventh, and eighth grades, present a variety of types of opera- 
tions, and are a test of power rather than a speed test. 

The Problem Tests were known to be unfamihar to the pupils. 
The form of II and III is such as to test for a minimum of control 
of vernacular and a maximum of control of operations and math- 
ematical reasoning. 

The Trabue Completion Tests represent the scientifically de- 
rived results of much careful testing. Dr. Trabue says of them, 
"It will be found that ability to complete these sentences suc- 
cessfully is very closely related to what is usually called 'language 
abiUty'." (25, p. 1) 

Thorndike Reading Scale Alpha 2 is a scientifically sound scale 
for the measurement of paragraph reading. The only limitation 
is that there are not other comparable scales available. 

Composition. A letter was chosen as one form of composition 
because it is commonly taught in schools and is the most ordi- 
nary form of writing done outside of school. The topic, "The 
Study I Like Best and Why, and the Study I Like Least and 
Why,"^ was chosen as furnishing a theme on which every child 
had something to say and as giving scope for the more capable 
pupils. 



iThis topic is suggested to teachers as of particular value from the standpoint 
of throwing light on the "content of children's minds" with respect to their 
studies. There is, no doubt, an advantage in having the test given by an 
outsider as the pupils tested gave evidence of more frankness than might be 
expected from them if writing for the teacher to read. 



The Data 23 

The Ayres Spelling Scale furnishes a comparatively large list 
from which to choose, and hence one less hkely to have been 
drilled upon. Column "U" was chosen as representing a degree of 
difficulty not altogether beyond reasonable attainment by the 
sixth grade and yet such as to test the eighth, 

d. To supplement these with a varied selection of psychological 
tests. Being tests involving knowledge of verbal relations, 
they serve to extend the scope of the English group. 

Opposites tests have been often shown to be very satisfactory 
tests as a measuie of the control of the vernacular. 

Visual Vocabulary tests supplement testing of paragraph read- 
ing. They are found to rank high as measures of "language 
power." 

Directions tests furnish a very real test of power to get meaning 
from a printed page. 

The other controlled association tests used had no particular 
claim except as supplementary to the others. 

3. Administration of the Tests 

Uniformity of Procedure. 

The aim in this study being a comparison of achievements in 
the different grades tested, it was of primary importance that 
the procedure in giving the tests be uniform throughout. Consid- 
ering the number of tests used, the number of schools, rooms, 
and classes concerned, involving numerous repetitions, the neces- 
sity for rigid control of conditions during the testing is obvious. 
To this end the following procedure was maintained throughout. 

a. Every test exercise was started by the writer. 

b. The writer remained in the room throughout the first test. There- 
after, except in the case of the short tests, he went to another room 
leaving an assistant to receive the papers and record the time on each. 

c. Either the writer or an assistant was in the room throughout each test. 

d. The teacher was regularly present, but ordinarily engaged in other 
work at the rear or side of the room. The very best of cooperation 
on the part of the teachers made possible very rigid control of the con- 
ditions in the room so far as any possible influence on the work of the 
pupils by the teachers was concerned. It was thoroughly understood 
from the beginning that all directions were to come from the testers. 
On the other hand the presence of the teacher in the room was a real. 



24 The Overlapping of Attainments in Certain Grades 

though unadvertised, help in insuring independent work on the part 
of each pupil. It is a pleasure, incidentally, to record the fact that 
the pupils were remarkably free from any tendency to depend on 
others for aid. 

e. At the very start of the testing in each room the mechanics of pro- 
cedure in the way of provision of pencils in good condition, clearing 
of desks, passing of papers, putting on of headings, signal for begin- 
ning and procedure on finishing the test, were fixed by rigid adherence 
to a pre-arranged plan, with modifications only to suit the needs of 
different tests. 

/. Preliminary to the beginning of each test specific directions to be given 
the pupils were worked out. These were adhered to carefully through- 
out. Any slight changes in general procedure were made at the be- 
ginning of a test, the aim being to maintain the very same procedure 
throughout all the rooms for a given test. 

g. The same order of tests was followed in all rooms with only a few 
slight changes made necessary by the time schedule. 

h. Special care was taken that those tests which by the nature of their 
content might easily become matter of common knowledge among the 
pupils of a school, such as spelling for example, were given during the 
same day's session. 

I. At the cost of considerable time no test was begun at such a time as 
would not insure ample opportunity for all to finish before an inter- 
mission as for recess or the noon hour, except in a very few cases where 
the custom of the room was well established to finish any given task 
even after other classes had been dismissed. 

Special Features. 

Spelling. Twenty sentences were framed, each containing one 
of the twenty words of the list, care being taken to use such a 
construction that the word could not be mistaken. These sen- 
tences were used throughout the testing. Previous to the test 
period papers with the regular heading and numbered from 1 to 
20 at the left-hand margin, had been prepared by the pupils under 
the direction of the teacher. The following directions were given : 
"I shall pronounce a word; then use it in a sentence; then pro- 
nounce it once more. Don't write anything until I have done these 
three things. 

"When you are all through with one word I shall say, 'Next.' If 
anyone is not ready, raise your hand. When all are ready I shall give 
the number of the next word. Make sure that when I say 'two' you 
are writing the second word. If you can't write some word leave its 
place blank. 

"Write plainly. What I can't read is called wrong, and there is 
some writing I can't read." 



The Data 25 

Reading. The Thomdike Reading Scale Alpha 2 is printed on 
two large sheets. The exercise headed Set IV, the last one on the 
first sheet, is repeated as the first exercise on the second sheet. 
In order to make sure that the pupils would not spend time on 
this second copy of Set IV, that part of the second sheet was cut off. 

Headings. Contrary to the usual practice the headings were 
put on the back side of the test papers. This insures that on the 
signal to begin all start work on the test material, and eliminates 
the variation in the length of time required to write the heading, 
as a source of error. 

Distribution of Papers. All test papers were distributed, al- 
ways with the printed side down and the top end away from the 
pupil, by the testers. This makes for a saving of time and regu- 
larity of procedure. 

Timing. As the time element is not made a feature of this 
study only a brief statement will be made regarding the timing of 
the tests. The following directions were given : 

"You will all begin at the same time. When you have done everything as 
well as you can, bring your paper to the desk." 

The time for each paper was recorded in minutes and seconds at 
the moment it was laid on the timer's desk — the teacher's desk 
in the front of the room. In case of the very short tests two timers 
were used in order to avoid delay in recording. In a group test 
without a time limit there is an unavoidable source of error in 
getting each individual's time recorded. It was decided this 
could be reduced to the minimum by taking the time at which the 
paper was put on the timer's desk. This method works a slight 
injustice to those in the rear of the room, but results in no constant 
error. 

The Tests as a Real Measure of Capacity. 

The statement was made at the beginning of this chapter that 
much of whatever value this study might have would hinge upon 
the extent to which each pupil was given an opportunity to show 
his real capacity in each test. To this end no test was given as 
a speed test; each pupil was given as much time as he wished. 
The assumption here is that in this way we get a much more ac- 
curate measure of what each pupil actually is capable of doing in 
his work from day to day. Our belief is that very Httle of the 



26 The Overlapping of Attainments in Certain Grades 

work on which his grade standing is based counts speed as an 
important factor. Ordinarily there is ample time for the tasks re- 
quired. We do not raise the question as to whether this is as it 
should be. Our purpose is to compare the attainments of differ- 
ent school grades as they exist. 

However, while it was the intention to allow the pupils all the 
time they needed, some stimulus against the waste of time was 
necessary in the interest of economy. This was provided by the 
fact that the pupils knew their time was recorded. There cer- 
tainly was some tendency to undue haste especially in the short- 
er tests. Except for a few of these short tests (the B-C group), 
however, the writer is confident this was a negligible factor. Early 
in the testing the practice of turning to other work as soon as a 
test was finished was well established among the pupils. As a 
result little was known as to who was not through with the test 
and hence no particular social disapproval was attached to slow- 
ness. The further fact that all the pupils had been subjected to 
testing under controlled conditions made the experience not un- 
like regular school work. 

In the case of the longer tests, as for example Alpha 2, in order 
not to interfere too much with the regular schedule, pupils who 
had not finished within a reasonable time were taken to an un- 
occupied room and there permitted to finish. 

Another factor making for an adequate measure of the attain- 
ments of the pupils was the large number of occasions on which 
the testing was done. The number of half-days during which one 
or more tests were given was 10, 11, 15, and 17 respectively for 
the different schools. This fact tends to offset the error which 
comes from using a single day's results as the measure of a pupil's 
standing. None of us care to be judged on the work of a single 
day, and with good reason. The following statement by Pro- 
fessor HoUingworth (12) brings out the significance of this point: 
"The momentary ability revealed in initial trials, or even in the 
first half dozen trials in a given set of tests might well be expected 
to show only low degrees of correlation. These would not be 
measures of ultimate capacity, but would be highly determined 
by previous practice, chance variabiHty, momentary attitude and 
initial method of attack. They would, in short, be samplings only 
of momentary ability, not of final capacity." 



The Data 27 

4. Scoring the Tests 

Consistency in the scoring of test papers is perhaps only second 
in importance to uniformity of procedure in giving the tests. 
This calls for particular care when the number of test papers in 
a given test is so large as to make impossible their scoring at one 
sitting, or indeed at a half dozen, but requires many sessions even 
though long. Furthermore, the large number of papers makes 
practically impossible the scoring by one person. Hence the need 
of careful supervision and accurate recording of method from the 
beginning to be followed throughout a given test. Of course the 
difficulty in scoring consistently is far less in the case of tests of 
the right or wrong sort, than in the case of those calling for partial 
credit and involving judgment; but even in the former the pos- 
sibility of error in a large number of tests is considerable. 

All the test papers in this study were scored by the writer or 
under his direct supervision. By far the larger part of the scoring 
was done by three readers, three others having done a small part. 

The purpose being to get results comparable with each other 
rather than with previously obtained data, no particular effort 
was made to use methods absolutely identical with those used 
elsewhere. This was at times sacrificed for the much more im- 
portant consideration of consistency throughout this study. 
However, for the benefit of any who may wish to compare other 
results with those here presented the following statement is made 
of the method of scoring. 

Woody Arithmetic Scales 

Score: Number of examples correct 

Problems 

Score: Number of points on basis of 
3 for full credit 
" [ for partial credit 

for no credit 

The answer recorded in the place assigned was the criterion used. 

Trabue 

Score: Number of points on basis of 
2 for full credit 

1 for partied credit 
for no credit 



28 The Overlapping of Atlainments in Certain Grades 

Composition 

a. The composition on the topic, "The Study I Like Best and Why and 
the Study I Like Least and Why" was scored with the use of the 
Thorndike Extension of the Hillegas Scale. (23) 

b. The letters were scored by means of an improvised 'scale.' Briefly 
the method of preparing this 'scale' was as follows. Forty papers 
were selected from the lot, representing in the judgment of the 
writer the whole range of ability from the poorest to the very best. 
It was not assumed that this number of different quahties could be 
detected. This large number was selected with the purpose of getting 
all grades of quahty. Five competent judges then ranked the papers 
according to the directions below: 

"Please rank the papers in eight groups of five each calUng Group I 
the poorest and Group VIII the best. 

"Enter the number of each paper (appearing in the upper right hand 
corner) on the appropriate line below. 

"Note that you are not asked to rank the papers within each group. 

"Assuming arbitrarily the value 10 for Group I and the value 80 
for Group VIII, assign intervening values to the other groups. Enter 
these values at the left of the number of the group." 

From the results of these rankings a selection of eight papers was 
made, those being selected on which there was greatest agreement among 
the judges as to the group in which each belonged. Of two or three 
papers equally placed, that one was chosen which seemed to best Ct 
into the whole. The amount of agreement among the judges is indi- 
cated below: 

Number placed in same group by Number of judges 

2 5 

10 4 

10 3 

On the combined judgments of the five readers the values from 10 
to 80 by equal intervals of 10 were given to the compositions in the 
eight groups from the poorest to the best. This is a rough evalua- 
tion and lays no claim to scientific accuracy. But the results justify 
the use of the 'scale' for the purpose of this study. The aim was to 
overcome the difficulty which all readers have who try to use the 
Hillegas Scale to judge compositions in the form of letters. The ar- 
bitrary method of assigning values to the letters composing the 'scale' 
was with the purpose of getting values roughly comparable with those 
on the Hillegas Scale. 

In all the work of scoring the compositions the reader was ignorant 
of the grade in which a given composition was written, this being very 
essential if a comparison of results by grades is to be made. 

The scoring was done by three readers, each paper being scored by 
each reader independently of the others. This gave three scores for 
each paper or six scores for each pupil. The final score for each pupil 
was obtained by taking the median of these six measures. ^ 



The Data 29 

Thorndike Reading Scale Alpra 2 

Score: Number of correct responses. The key published by the author 
(20) was used, with additions as necessary. 
Spelling 

Score: Number of words spelled correctly 
Opposites 
Score: 3 for full credit 

Mor partial credit 
for no credit 

All the available keys were used. However, numerous answers had 
never been passed upon in these keys and it became necessary to ex- 
tend them greatly. This was done by using the combined judgments 
of from two to eleven judges. Because of the very great number of 
answers occurring only a very few times it was necessary in these cases 
to rely on the judgments of only two persons, the writer and one other 
in every case. 

Bl, B2, CI, C2, C3 
Score: 1 for full credit 

H for partial credit 
for no credit 

Dl, D2 

Score: Number of correct responses 
X 

Score: A, B, D, E, F were allowed 2 each when correct. C and G 
were allowed 1 for each line correct. 
VI 

Score: Number of correct responses 
VII 

Score: One point was allowed for each step correct except 31 and 32. 
These two steps were scored as a unit. The number right minus the 
number wrong, counting omissions, being the score. 
VIII 

Score: Number of correct responses 
XIII 

Score: Number of correct responses 



Ill 



OVERLAPPING BY SINGLE TESTS 

1. The Measure of Overlapping 

The measure of overlapping in this study is the per cent of the 
pupils in any grade who equal or exceed the median score of the 
next grade or the second grade above; or the per cent of the pupils 
in any grade who go below the median score of the next grade or 
the second grade below. The former will be referred to as over- 
lapping "upward" and the latter as overlapping "downward." 

The value of this measure of overlapping is shown in the follow- 
ing statements by Professor Thorndike, and by his accompany- 
ing diagrams. (21) "The great advantage gained by comparing 
groups by the per cent of one group reaching or exceeding the 
point on the scale that is reached or exceeded by a given per cent 
of the other group is that results are mutually comparable what- 
ever the traits may be . . . Another advantage lies in the 
fact that this percentile comparison reminds one constantly of 
the overlapping of the two groups, when such exists." 

The distributions on which the per cents of overlapping are 
calculated wiU be found in the Appendix. Table II shows the 
amount of overlapping in 21 tests, of the sixth grade on the eighth, 
the sixth on the seventh, and the seventh on the eighth, upward; 
and downward, the eighth on the sixth, the eighth on the seventh, 
and the seventh on the sixth. 



30 



Overlapping by Single Tests 



31 



TABLE II 

Overlapping of Grades by Single Tests 

Per cent in each grade who equal or exceed the median of the other grade; 

upward. Per cent in each grade who go below the median of the 

other grade; downward 

Upward Downward 

VI VI VII VIII VIII VII Average 

on on on on on on of the six 

Tests VIII VII VIII VI VII VI measures 

Addition 24.19 35.92 38.71 25.90 36.15 37.39 33.04 

Subtraction 22.30 25.66 44.22 19.90 42.09 25.77 29.99 

Multiplication 23.42 33.23 40.90 26.53 39.18 34.92 33.03 

Division 28.27 35.36 43.57 26.76 38.73 37.43 35.02 

Problemsl 7.14 13.31 32.77 9.63 33.49 18.45 19.13 

Problems II 10.64 16.95 36.06 14.04 37.19 25.29 23.36 

TrabueB 26.61 34.54 44.29 30.01 42.86 38.12 36.07 

TrabueC 21.68 38.49 34.65 25.28 33.32 40.05 32.25 

TrabueD 23.31 38.58 36.95 30.92 38.34 41.32 34.90 

TrabueE 13.99 36.86 25.91 19.74 26.97 37.16 26.77 

Alpha 2 11.61 28.02 31.99 12.73 33.00 26.49 23.97 

Spelling 7.37 21.09 30.26 7.39 26.34 22.14 19.10 

OppositesA2 8.76 19.37 36.57 14.08 35.44 23 65 22.98 

OppositesA3 13.33 31.80 28.44 14.16 26.41 32.82 24.49 

OppositesA4 10.05 22.18 3r.77 11.15 34.11 27.50 22.79 

Part-Whole C3 35.18 45.59 35.42 34.85 37.82 45.77 39.11 

Mixed Relations Dl... 42. 53 53.50 43.95 43.87 41.19 52.65 46.28 

Mixed Relations D2... 38. 75 48.67 39.50 34.60 35.84 49.07 41.07 

Directions VII 21.23 37.38 35.10 27.88 38.80 38.82 33.20 

Visual Vocabulary VIII 10.64 24.22 24.06 9.20 28.34 24.69 20.19 

VisualVocabularyXIII 11.06 26.53 29.94 11.41 28.29 23.40 21.77 

Average 19.62 31.77 35.48 21.43 34.95 33.47 29.45 

7.14 13.31 24.06 7.39 26.34 18.45 19.10 

Range to to to to to to to 

42.53 53.50 44.29 43.87 42.86 52.65 46.28 



The table reads- In addition 24. 19 per cent of the pupils in the sixth grade 
equal or exceed the median of the eighth grade; 38.71 per cent of the pupils 
in the seventh grade equal or exceed the median of the eighth grade; 25.90 
per cent of the pupils in the eighth grade go below the median of the sixth 
grade; and 36.15 per cent of the pupils in the eighth grade go below the 
median of the seventh grade. 



32 The Overlapping of Attainments in Certain Grades 

2. The Elimination of Some Tests 

The fact that there are figures for only 21 tests calls for explan- 
ation. It is the purpose to present the results for only those tests 
which proved to be fair measures for the three grades used, on the 
basis of the distributions of the scores for each grade. Some tests 
proved too easy with consequent piling up of undistributed scores 
at the upper end. The higher ranges of abihty were not measured. 
The way up was closed, so to speak. This naturally works to the 
greatest disadvantage of the eighth grade, to less for the seventh, 
and least for the sixth. The result is an unduly high per cent of 
overlapping upward. The closeness with which the grade med- 
ians approximate the total possible score is a rough measure of 
this exaggeration of the overlapping figures. For example, the 
median score of the sixth grade may be very near the maximum 
possible score, beyond which obviously none in the eighth grade 
can go. Table III has been prepared to show which tests are 
affected in this way. This table gives the median score for each 
grade in each test and the maximum possible score. With the 
purpose, then, of ruling out those tests which by their very nature, 
as shown in the distribution tables, make a high per cent of over- 
lapping inevitable, the tests Al, Bl, B2, CI, C2, X, VI are omitted 
from Table II. Problems III proved much too difficult with un- 
distributed scores at the lower end, and hence is not included.^ 
The two composition tests, the scores for which were not dis- 
tributed singly, do not appear in the table. Composition is 
treated only as a composite. 

It should be borne in mind in connection with the treatment in 
Chapter IV that the inclusion of the first eight tests mentioned 
above would have raised the average per cents of overlapping 
to higher figures. Hence any showing based upon the magnitude 
of the per cents of overlapping by single tests would have been 
magnified had these tests been included. There is no absolute line 
of demarcation between the tests that should and the tests that 
should not be used. The error, for the vafidity of the argument 
which follows in Chapter IV, could not have been in the direction 
of eliminating too many tests. 



^A table of per cents of overlapping for these tests is given in the Appendix. 



Overlapping by Single Tests 



33 



Tests 



VI 



Addition 29.30 

Subtraction 25 . 74 

Multiplication 27.84 

Division 24 . 54 

Problems 1 9.11 

Problems II 2.28 

Trabue B 13.37 

Trabue C 12.94 

Trabue D 14.20 

Trabue E 13 . 30 

Composition 37 . 66 

Alpha 2 22.61 

Spelling 12.73 

A 1 122.69 

A 2 53.71 

A 3 49.52 

A 4 48.45 

B 1 16.50 

B2 * 

C 1 29.28 

C 2 26.27 

C 3 15.34 

D 1 16.12 

D2 17.19 

X 14.69 

VI 19.43 

VII 10.17 

VIII 70.12 

XIII 75.38 



TABLE III 






'est for Each G 


RADE, WITH 


Maximum 


ssiBLE Scores 






Grades 




Maximum 


VII 


VIII 


possible 
score 


30.89 


32.35 


38 


28.37 


28.87 


35 


29.65 


30.69 


39 


26 06 


26.85 


36 


15.36 


18.35 


30 


5.06 


6.54 


18 


14 13 


14 57 


20 


13.57 


14.65 


20 


14 61 


15.32 


20 


13.93 


15.50 


20 


42.89 


49.27 


87.5 


25.37 


27.08 


38 


17.15 


18.97 


20 


126.19 


128.77 


138 


66.11 


73.44 


138 


56.50 


68.07 


138 


65.08 


73.37 


138 


18.29 


17.57 


20 


* 


* 


20 


29.62 


* 


30 


27.56 


28.31 


30 


15.71 


16.69 


20 


15.76 


16.85 


40 


17.45 


22.25 


40 


16.10 


16 11 


18 


19.55 


19.55 


20 


10.59 


11.33 


18 


78.10 


84.67 


100 


100.63 


119.35 


169 



3. Comparison of Different Tests as to Amount of 
Overlapping 

We have been prepared to find large amounts of overlapping 
and we find our results no exception. Less to be expected, per- 
haps, is the great range among the tests. It is obvious that were 
one making deductions from overlapping figures from single tests 



*See distribution tables in Appendix. 



34 The Overlapping of Attainments in Certain Grades 

much would depend upon the particular tests chosen. For ex- 
ample, any conclusions regarding overlapping in aiithmetic 
drawn from a per cent of 28.27 in division (VI on VIII) would be 
quite otherwise than if based on a per cent of 7.14 in Problems I. 
The possibility of error from inferences from such results as those 
presented in Table II is further illustrated by assuming that 13.99 
per cent (Trabue E) measures the overlapping of VI on VIII in 
Completion-Test Language Scales rather than 26.61 per cent 
(Trabue B). Much would thus depend upon whether one used 
one or the other of these tests, though they are of demonstrated 
equal difficulty. "Language Scales D and E are practically of 
the same difficulty as Scales B and C." (25, p. 22) 

In the discussion of the relative amounts of overlapping in the 
different tests which follows let it be borne in mind that we make 
no claim that these figures derived from single tests are valid 
measures of overlapping in the traits measured. The great range 
in the per cents for tests counted of equal difficulty has raised a 
feeUng of doubt, to say the least. Later we shall consider this 
question specifically. 

But taking these figures of Table II for just what they are, per 
cents of overlapping in the different tests as indicated, we shall 
see what an analysis of them reveals. 

Tables IV, V, and VI have been prepared as an aid in answer- 
ing the question, How do the tests rank in amount of overlapping 
as determined by the six sets of comparisons, three upward and 
three downward? 

Table IV lists the tests in order of rank from the least to the 
most overlapping, on each basis. 



Overlapping by Single Tests 



35 



TABLE IV 

Lists of the Tests in Order from the Least to the Most Overlapping for 
Each of the Six Comparisons 



VI 


VI 


VII 


VIII 


VIII 


VII 


Rank on 


on 


on 


on 


on 


on 


VIII 


VII 


VIII 


VI 


VII 


VI 


1 Problems I 


Problems I 


VIII 


Spelling 


Spelling 


Problems I 


2 Spelling 


Problems I] 


[ Trabue E 


VIII 


A3 


Spelling 


3 A2 


A2 


A3 


Problems I 


Trabue E 


XIII 


4 A4 


Spelling 


XIII 


A4 


XIII 


A2 


5 


A4 


Spelling 


XIII 


VIII 


VIII 


5.5 Problems II 












VIII 












6 


VIII 


A4 


Alpha 2 


Alpha 2 


Problems II 


7 XIII 


Sub. 


Alpha 2 


Problems II 


Trabue C 


Sub. 


8 Alpha 2 


XIII 


Problems I 


A2 


Problems I 


Alpha 2 


9 A3 


Alpha 2 


Trabue C 


A3 


A4 


A4 


10 Trabue E 


A3 


VII 


Trabue E 


A2 


A3 


11 VII 


Mult. 


C3 


Sub. 


D2 


Mult. 


12 Trabue C 


Trabue B 


Problems II 


Trabue C 


Add. 


Trabue E 


13 Sub. 


Div. 


A2 


Add. 


Problems II 


Add. 


14 Trabue D 


Add. 


Trabue D 


Mult. 


C3 


Div. 


15 Mult. 


Trabue E 


Add. 


Div. 


Trabue D 


Trabue B 


16 Add. 


VII 


D2 


VII 


Div. 


VII 


17 Trabue B 


Trabue C 


Mult. 


Trabue B 


VII 


Trabue C 


18 Div. 


Trabue D 


Div. 


Trabue D 


Mult. 


Trabue D 


19 C3 


C3 


Dl 


D2 


Dl 


C3 


20 D2 


D2 


Sub. 


C3 


Sub. 


D2 


21 Dl 


Dl 


Trabue B 


Dl 


Trabue B 


Dl 



36 



The Overlapping of Attainments in Certain Grades 



Table V summarizes the facts of Table II on the basis of divi- 
sion into tertiles. It shows that Spelling and VIII fall in the 
lowest third in all six comparisons, no test fcJls in the middle and 
only one test, Dl, falls in the highest third in the six comparisons. 
One test, XIII, falls in the lowest third in five comparisons, and 
three tests, A4, Problems II, and Problems I, fall in the lowest 
third in four comparisons. At the other extreme we have one 
test, Dl, in the highest third in six comparisons, and so on. It 
appears therefore that there is most agreement among the differ- 
ent comparisons in placing Dl at the top of the list in amount of 
overlapping, and Spelling and YIII at the bottom of the list, that 
is, with least overlapping. 

TABLE V 

Showing What Tests are in the liOWEST, Middle and Highest Thirds 

AS TO Amount of Overlapping in Four or More of the Six 

Comparisons, VI on VIII, VI on VII, etc. 

In six In five In four 

comparisons comparisons comparisons 



In 

lowest 
third 


Spelling 
VIII 


In 

middle 

third 


None 


In 

highest 

third 


Dl 



XIII 



None 



Trabue B 
D2 



A4 

Problems II 
Problems I 

A3 
Addition 



Division 
C3 
VII 
Trabue D 



Table VI furnishes another basis for measuring the relative 
amount of overlapping for the different tests. A rank is given 
each test in each of the six comparisons. These ranks are added 
and another ranking made in column 8. A ranking in column 9 
is made on the basis of the averages from the six measures. (See 
Table II, last column.) Finally these two rankings are added and 
the rankings of column 11 obtained, which may be taken as the 
order of the tests in amount of overlapping on this basis. From 
the combined results then, the following tests show the least 
amount of overlapping, roughly in the order named: Spelling, 
Problems I, VIII, XIII, A4, A2, Alpha 2. 



Overlapping by Single Tests 



37 



TABLE VI 







Rankings of the T 


'est.s 1 


[N Amount 


OF Overlapping 








1 


2 


3 


4 


5 


6 


7 
Sums 


8 
Rank- 


9 
Rank- 
ings 


10 

Sums 


11 

Final 
Rank- 






1 


Comp 


larisons 




of 


ings 


of 


of 


ings 
















Rank- 


of 


Aver- 


Rank- 


of 




VI 


VI 


VII VIII VIII VII 


ings 


Totals 


ages 


ings 


Totals 


Tests 


on 


on 


on 


on 


on 


on 


of 


in 


of 


of 


in 




VIII VII VIII VI 


VII 


VI 


Columns 


Column 


Table Columns 


Column 
















lto6 


7 


II 


8 and 9 


10 


Problems I . 


. 1 


1 


8 


3 


8 


1 


22 


2 


2 


4 


2 


Spelling.... 


. 2 


4 


5 


1 


1 


2 


15 


1 


1 


2 


1 


VIII 


. 5.5 


6 


1 


2 


5 


5 


24.5 


3 


3 


6 


3 


XIII 


. 7 


8 


4 


5 


4 


3 


31 


4 


4 


8 


4 


A4 


. 4 


5 


6 


4 


9 


9 


37 


5 


5 


10 


5 


A2 


. 3 


3 


13 


8 


10 


4 


41 


6 


6 


12 


6 


Alpha 2.... 


. 8 


9 


7 


5 


6 


8 


43 


7.5 


8 


15.5 


7 


Problems II 


. 5.5 


2 


12 


7 


13 


6 


45.5 


9 


7 


16 


8 


A3 


. 9 


10 


3 


9 


2 


10 


43 


7.5 


9 


16.5 


9 


Trabue E. . 


.10 


15 


2 


10 


3 


12 


52 


10 


10 


20 


10 


Trabue C. . 


.12 


17 


9 


12 


7 


17 


74 


11 


12 


23 


11.5 


Sub 


.13 


7 


20 


11 


20 


7 


78 


12 


11 


23 


11.5 


Mult 


.15 


11 


17 


14 


18 


11 


86 


14.5 


13 


27.5 


14 


VII 


.11 


16 


10 


16 


17 


16 


86 


14.5 


15 


29.5 


15 


Trabue D.. 


.14 


18 


14 


18 


15 


18 


97 


17 


16 


33 


16.5 


Add 


.16 


14 


15 


13 


12 


13 


-83 


13 


14 


27 


13 


Div 


.18 


13 


18 


15 


16 


14 


94 


16 


17 


33 


16.5 


Trabue B . . 


.17 


12 


21 


17 


21 


15 


103 


19 


18 


37 


18.5 


C3 


.19 


19 


11 


20 


14 


19 


102 


18 


19 


37 


18.5 


D2 


.20 


20 


16 


19 


11 


20 


106 


20 


20 


40 


20 


Dl 


.21 


21 


19 


21 


19 


21 


122 


21 


21 


42 


21 



4. Surfaces of Overlapping 

Figs. 1 to 4 show in graphic form the overlapping of the three 
grades in tests Trabue B, Opposites-A2, Part-Whole^C3, and 
Division. These surfaces are all drawn of equal area and on the 
same base Une, so that they are directly comparable one with 
another. The vertical distance represents the per cent of each grade 
attaining the scores indicated on the horizontal. The surfaces 
are for the sixth, seventh, and eighth grades from the bottom up 
in every case. The medians are drawn for each grade through 
the surfaces of the other grades so as to faciUtate comparison. 
The measure of overlapping is represented by the portion of the 
surface of a given grade which extends beyond the median of the 



38 



The Overlapping of Attainments in Certain Grades 



grade with which comparison is made. For example, in Fig. 1 the 
area ABC, 34.54 per cent of the whole, represents the part of 
the sixth grade that reaches or exceeds the median of the seventh; 
and the area DBE, 26.61 per cent of the whole, represents the 
part of the sixth grade that reaches or exceeds the median of the 
eighth. Likewise, the area AiBiCi, 30.01 per cent, represents 
the part of the eighth grade that goes below the median of the 
sixth; and the area DiBiEi, 42.86 per cent, represents the part of 
the eighth grade that goes below the median of the seventh. 

These figures give us also a representation of the form of dis- 
tribution for these tests. Figs. 1, 2, and 4, for example, approxi- 
mate rather closely to the "normal" curve, in contrast with Fig. 3, 
which shows considerable skewness toward the upper end. It was 
this condition still more emphasized that made advisable the elim- 
ination of some of the tests. 



Grade Vlll 




g 12 A D 16 B 30 

Fig. 1. Overlapping in Trabue B. 



Overlapping by Single Tests 



39 



Grade Viii 




26 50 75 100 

Fig. 2. Overlapping in A-2, Opposites. 



40 The Overlapping of Attainments in Certain Grades 



Grode VIII 




4 8 12 16 SO 

Fig. 3. Overlapping in C-3, Part-Whole. 



Overlapping by Single Tests 



41 




GraJe Vill 



Grade vii 




Grade vi 



n_r 



A]-! 



fl., 




n 



10 16 22 28 34 

Fig. 4. Overlapping in Division. 

The results presented in this chapter are in accord with those 
reported in the Introduction as showing great variability within 
the grades and consequent overlapping among the grades, when 
attainment is measured by single tests. Certainly measurements 
of this sort show large amounts of overlapping even when given 
under well-controlled conditions and to large numbers of pupils. 
We are now ready to consider the question raised at the beginning: 
Are measures obtained in this way valid measures of the over- 
lapping of ability of school pupils in different grades? The 
next chapter wiD consider this problem. 



IV 

OVERLAPPING IN THE CASE OF COMPOSITES 

1. Results 

Suppose a single test be given to sixth- and eighth-grade pupils 
with a resulting overlapping of the sixth on the eighth of 25 per 
cent. Are we justified in using this figure as a measure of the 
overlapping of abilities in the trait measured? Only in so far, 
of course, as this single test is a measure of the trait. Suppose 
that in order to get a more valid measure of overlapping we give 
three more tests of the same sort and use the average of the four 
as the measure. This will tend to even up any extreme results 
from a particular test. Rut this average will retain any error 
resulting from the inadequacy of a single test as a measure of the 
trait in question. It does not take account of the fact that the 
pupil who is in the lowest quartile in one test may be in the high- 
est quartile in the second test, and still differently placed in the 
third and fourth tests. In proportion as the single test is an ade- 
quate measure of a trait, a pupil's place in the distribution wiU 
be the same in the different test exercises (except in so far as par- 
ticular conditions affecting the pupil at a given time influence the 
result). In order to give the individual pupil the benefit of more 
nearly adequate testing, a composite may be made of the differ- 
ent scores he makes in the different tests for a given trait and this 
used as his measure. Thus any error in his placing in the dis- 
tribution resulting from only a single test tends to be offset by 
the other measures. The principle of procedure here is simply 
that up to an undefined Hmit the larger the number of measures, 
the greater the accuracy of placing the individual where he be- 
longs in the distribution. Theoretically, then, the amount of 
overlapping as measured in single tests should be reduced when 
taken in terms of the composite. 
42 



Overlapping in the Case of Composites 43 

TABLE VII 
Overlapping of Grades by Composites 

Per cent in each grade who equal or exceed the median of the other grade; upward. 
Per cent in each grade who go below the median of the other grade; downward 
Upward Downward 

No. VI VI VII VIII VIII VII Average 

of on on on on on on of the six 

Composites Tests VIII VII VIII VI VII VI measures 

Composition 2 13.64 27.86 24.09 8.02 21.26 24.95 19.97 

Trabue 4 14.68 32.46 31.19 21.89 31.75 36.63 28.10 

Opposites 3 8.57 24.87 30.49 13.41 29.58 26.97 22.32 

B-C ■ 5 32.59 32.62 44.21 36.07 49.99 41.40 39.48 

Mixed Relations 2 39.51 51.40 41.32 40.25 39.17 .50.69 43.72 

Directions 3 27.38 31.67 45.30 29.64 45.42 31.96 35.23 

Visual Vocabulary... 2 8.32 22.48 28.14 11.35 27.31 26.81 20.74 

Arithmetic 6 7.08 18.13 33.21 12.00 32.68 24.28 21.23 

English 22 6.97 24.86 25.83 9.68 23.18 26.12 19.44 

Total 28 4.58 19.57 27.74 8.37 24.15 21.98 17.73 

Table VII presents the facts of overlapping when the scores are 
thus combined for the diiferent groups of tests and redistributed. 
Table VIII brings together the data of Tables II and VII in such 
a vs^ay as to permit a comparisoi* of the results obtained by aver- 
aging the per cents of overlapping for the different tests of a group 
with those obtained from this method of composites. It will be 
seen, for example, that in the Vl-on-VIII comparison the average 
per cent of overlapping for the four Trabue tests, 21.40, is re- 
duced to 14.68 for the composite, a reduction of 6.72 points. 
Column "d" shows the difference between the two measures of 
overlapping, the " — " prefix indicating a reduction for the com- 
posite method. The totals for the "d" columns show that the 
few cases of the reverse order, an increase for the composite meth- 
od, represent a very, very small portion of the total difference. 
Further analysis of the table reveals some interesting facts. The 
greatest difference in the two methods is found in the Vl-on-VIII 
comparison, and the least in the Vll-on-VIII comparison, the 
two in which the per cent of overlapping was, on the other hand, 
the least and the greatest, respectively. (See Table II.) The 
difference is small in the case of those composites representing 
a small number of tests such as Mixed Relations and Visual 
Vocabulary, of only two tests each. The arithmetic composite 
of the results from six tests is consistently lower than the average, 



44 



The Overlapping of Attainments in Certain Grades 



o ^ o 



i2 



Overlapping in the Case of Composites 



45 



2 § 



■■3 -9 



OS 


VO 


(N 


,-^ 


ir> 


t- 


CO 


X 


7 


cj 


a 
c 


! 






o 


a 






'0 


<! 








OJ 






o 


^ 






'i2 








2 


i 





1 


M 


c 
o 


S S 


J 


«2 


CO 


?^^ 


^ 

c 


c 


a 



. u 



o Ji 

a = 



-S ^ F 



M ^ ja 



46 The Overlapping of Attainments in Certain Grades 

the difference ranging from 5.13 for VIII on VII to 12.25 for VI 
on VIII. So also the EngUsh composite of sixteen tests shows a 
reduction of from 7.47 to 12.39 below the average. 

Most significant of all the figures are those for the total com- 
posite. The reduction here represents a range from 7.22 to 14.77, 
with five out of the six measures above 10.00. The results are 
summarized in Table IX. 

TABLE IX 

Showing the Per Cent of Reduction of the Overlapping in the Total 

Composite as Compared with the Average of 22 Tests 

Average Total Per cent of 

Comparisons of 22 tests composite reduction 



VI on VIII 


19.35 


4.58 


76 


VI on VII 


31.59 


19.57 


38 


VII on VIII 


34.96 


27.74 


21 


VIII on VI 


20.82 


8.37 


60 


VIII on VII 


34.33 


24.15 


30 


VII on VI 


33.08 


21.98 


34 



Table IX reveals the amount of error that would have resulted 
had we used the results from single tests as a measure of over- 
lapping of Grades VI, VII, and VIII. The error would have been 
greatest in the Vl-on-VIII comparison and least on the Vll-on- 
VIII, as shown by the fact that the per cent of overlapping is 
reduced 76 per cent in the former, and 21 per cent in the latter. 
The facts of Table IX show very clearly the limitations of the 
results from single tests as measures of overlapping, and illustrate 
the necessity of careful scrutiny of any general statements re- 
garding the amount of overlapping of grades based upon such 
data. 

Our results permit an answer to the question. How do the dif- 
ferent grades tested compare with each other as to amount of 
overlapping.^ As might be expected, the overlapping in the case 
of the sixth and eighth grades is least. It might not have been 
anticipated, however, that the overlapping in the case of the 
seventh and eighth grades would exceed that of the sixth and 
seventh. Nevertheless it does so generally throughout. 

Inspection of Table VII reveals the fact that the overlapping 
of Grades VII and VIII exceeds that of Grades VI and VII in 
12 out of the 20 cases, upward and downward. This excess in 
the per cent of overlapping of Grades VII and VIII is brought 



Overlapping in the Case of Composites 47 

out more markedly when the magnitude of these differences is 
taken into account. The totals show an excess for Grades VII 
and VIII over Grades VI and VII of 96.45 as against 38.15 ex- 
cess for Grades VI and VII over VII and VIII. That is, on the 
basis of the results by composites, Grades VII and VIII show an 
amount of overlapping in excess of that of Grades VI and VII 
about three times as great as that of Grades VI and VII over VII 
and VIII. A similar relation, though in reduced amount, holds 
in the results from single tests, as may be seen from Table II. 

These facts seem to furnish some substantial evidence in sup- 
port of the generally accepted notion that the work of the sev- 
enth and eighth grades is less clearly differentiated than that of 
the sixth and seventh. They appear to support the contention 
that the eighth grade is largely only a transition period. If so, 
they add weight to the argument for modification of ouf school 
grading scheme. It may also prove to be significant, especially 
for departmental teaching, that although Grades VII and VIII 
show more overlapping on the whole. Grades VI and VII show 
an excess in Composition, Trabue and Mixed Relations. (See 
Table VII.) 

Summarizing, we may say tl^fit the amount of overlapping 
measured by a single test is reduced appreciably when measured 
by a composite of a number of tests of the same trait, there being a 
direct relation between the number of tests entering into the com- 
posite and the amount of reduction. Moreover, when a further 
grouping of scores is made by recombining these composites of 
single tests in a given trait into a gross composite representative 
of ability in a more complex trait, as, for example, control of the 
vernacular as exemphfied in our English composite of 22 tests, 
the amount of overlapping is appreciably reduced. Extending 
this grouping so as to include a composite of results from tests of 
a still different trait, such as arithmetic, we get still more reduc- 
tion of the overlapping in this complex, more nearly representative 
of school ability. 

2. Surfaces of Overlapping 

Figs. 5 to 10 show the distribution surfaces and resulting over- 
lapping of Grades VI, VII, and VIII in several of the composites, 
as an aid in understanding the facts of Table VII. The arrange- 
ment of the surfaces is similar to that of Figs, t to 4, previously 



48 



The Overlapping of Attainments in Certain Grades 



explained.! The figures are in order from greatest to least over- 
lapping, roughly shown by the differences between the medians. 
Fig. 11 has been drawn in the form of smooth curves as a basis 
for comparison. The lower set of curves shows the amount of 
overlapping of Grade VI on Grade VIII in the total composite, 
4.58 per cent, in contrast with the upper set of curves which shows 
the amount of overlapping of these grades in the average for 22 
tests, 19.35 per cent. (See Table VIII.) The figure thus illus- 
trates the amount of reduction by the composite method over 
the^results from single tests. 



" 


' "V 


VUI 










J 






























r 














1 






1 


1 












Grade vil 








1 


— 1 




















Grade vi 


r^ 








.^_ ._J^ 
















■■ 





30 36 42 48 

Fig. 5. Overlapping in Directions Composite. 



Overlapping in the Case of Composites 49 



Grade VIII 



Gra6e vii 



Grade vi 



26 36 45 65 65 75 

Fig. 6. Overlapping in Trabue Composite. 



50 The Overlapping of Attainments in Certain Grades 



VI V I vm 



Grade vi 




Grade VII 





Grade vi 



1 



70 95 120 146 170 

Fig. 7. Overlapping in Arithmetic Composite. 



Overlapping in the Case of Composites 51 



V,l V 


1 


i/iii 










1 
















Crais VIII 


_ 












^ 






































Grode VII 
















- 
















1 


































Grade vi 


















































I 





30 46 60 75 

Fig. 8. Overlapping in Composition. 



52 The Overlapping of Attainments in Certain Grades 



Grade vill 



VI VII m 



^ 



Grade VII 



Grade vi 



leO 260 340 420 600 

Fig. 9. Overlapping in English Composite. 



Overlapping in the Case of Composites 53 



Grade V 




SeO 460 560 660 760 

Fig. 10. Overlapping in Total Composite. 



54 



The Overlapping of Attainments in Certain Grades 




Fig. 11. 

A. Overlapping of Grade VI on Grade VIII in the Average for 22 Tests, 

19.35 Per Cent. (See Table VIII.) 

B. Overlapping of Grade VI on Grade VIII in the Total Composite, 

4 58 Per Cent. (See Table VIII.) 

3. Statistical Treatment 
Weighting of Tests. 

In making the first group of composites each test entering into 
a given composite was counted equal in value to every other. For 
example, Addition, Subtraction, Multiplication, Division, Prob- 
lems I, and Problems II were counted of equal value as units in 
the arithmetic composite. Therefore, the scores of a given pupil 
in these six tests were added and the sum taken as his score in 
arithmetic. Similarly in Trabue the scores in the four tests were 
added, and in Opposites the scores for three tests. A B-C com- 
posite was made by adding the scores in Bl, B2, Cl, C2, C3. 
Mixed Relations is a composite of Dl and D2; Directions of X, 
VI, and VII; and Vocabulary of VIII and XIII. 

However, in making the composite for all the English tests it 
became necessary to recognize statistically what common sense 
demands, that one of these composites may have more or less 
value than another as a unit in a total English composite. Like- 
wise in the final total, including all tests of both groups. Arith- 
metic and English, each composite had to be given a value. 



Overlapping in the Case of Composites 55 

This involved three steps: (1) calculating a measure of vari- 
ability for each group of tests and each single test in each grade; 
(2) determining upon the relative weight to be given to each com- 
posite group or single test in a composite; (3) multiplying or 
dividing (as the case required) the scores in a given composite 
by the factor necessary to bring them to a basis comparable with 
ail the others. 

It was found that the standard deviations (the measure of 
variabihty used) for the three grades varied one with another 
throughout the different tests so Uttle that the average of the three 
S. D.'s for a given test was used. 

In determining upon the weights to be given to the different 
tests the combined judgment of eight judges, familiar with the 
tests, was used. Table X shows the weights given and the factor 
by wliich the scores in each group of tests or in each test were 
multiplied or divided. 

TABLE X 

Weights Given to Single Tests and to Groups of Tests Entering into 
THE Engush Composite and the Total Composite 

S. D. 

No. of Average Multiple Weight 

tests for the given 

3 grades 

Spelling 1 4.43 X 1 = 4.43 

Alpha 2 1 3.84 X 2 = 7.68 

Composition 2 8.07 X 1 = 8 . 07 

Trabue 4 7.17 X 2 = 14.34 

Opposites 3 54 . 13 

B-C 5 17.61 

Mixed Relations 2 16.51 

Directions 2 4.09 X 1 = 4.09 

Vocabulary 2 39.70 -h 5 = 7.94 

Arithmetic 6 19.20 X 2 = 38.40 

Interpolated Scores. 

The following rules were followed in supplying missing scores: 
1. In arithmetic interpolations were made if not more than 

three out of the six scores were lacking. The median score for 

the particular class was used, rather than the median for the 

whole grade. 



5 = 10.83 
4 = 4.40 

2 = 8.26 



56 The Overlapping of Atlainments in Certain Grades 

2. If only one composition was written the score for this was 
neglected and the median for the class for both compositions 
was used. 

3. In the B-C composite interpolations were made when not 
more than two scores out of the five were missing. 

4. In the Mixed Relations composite when one score was 
missing the score for the other test was used, as the central 
tendencies for the two tests are practically equal. 

5. In all cases of single tests, e.g., Alpha 2 £ind Spelling, the 
medians for each class were used. 

6. In the total English composite interpolations were made if 
not more than four out of the nine scores were missing. 

7. In the total composite a missing score in mathematics was 
interpolated when not more than two others, in the English 
group, were interpolated; five scores were interpolated in the 
English group if the mathematics score was present. 



RELIABILITY OF THE TESTS USED AS DETERMINED 

BY THE CORRELATION OF GROUPS OF 

SIMILAR TESTS 

So far we have been attempting to measure the amount of over- 
lapping of attainments in certain sixth, seventh, and eighth 
grades by the use of more or less well standardized tests. It is 
our purpose in this chapter to apply a measure of reliability to 
the tests we have used, the results of which should serve the two- 
fold purpose of measuring the validity of our results and serve as 
a guide to any who may wish to know how much reliance may 
be placed in certain tests as measures of attainment in Grades 
VI, VII, VIII. 

Most of the work heretofore done in the way of measuring the 
reh£ibility of given tests as measures of general mental ability has 
been by means of correlations among the tests, but with single 
or, at most, very few measures by a given test. Our data furnish 
a particularly good opportunity to supplement these results, as 
we have the advantage of comparison by composites, thus tend- 
ing to overcome the error resulting from the use of only one or 
two tests of a given trait. Further we have the very real advan- 
tage of large numbers. While this latter gives greater validity 
to the results obtained, it makes the calculation of many coeffi- 
cients of correlation prohibitive because of the amount of labor in- 
volved. We have chosen one comparison of two groups of tests 
in arithmetic and one of two groups of tests in Enghsh. 

Two Arithmetic composites were made by adding the scores in 
addition, division and the first problem test for the one, and sub- 
traction, multiplication, and the second problem test for the 
other. Likewise two English composites were made. The first 
was composed of the scores in the Trabue, Opposites, B-C, and 
Visual Vocabulary composites and the second, of those in the 

57 



58 



The Overlapping of Attainments in Certain Grades 



Composition, Reading, Mixed Relations, and Directions com- 
posites. Each was weighted as indicated above. 

Coefficients of correlation were then calculated by the Pearson 

method, formula r = — ==r--=^, for each group of composites, for 

V Lot V Ly 

each grade, with the results indicated below. 

TABLE XI 

Coefficients of Correlation Between Arithmetic Composites and 
BETWEEN English Composites 



Arithmetic 

One group of three tests with 

another group of three 

No. 

Grade of pupils r 

VI 240 .706 

VII 310 .774 

VIII 275 .713 



English 

One group of five tests with 

another group of five 

No. 
of pupils r 

256 .739 

325 .749 

283 .705 



Average .731 .731 

From these coefficients of correlation we are able, by the use of 

Rrown's formula (3), to get a measure of the reUability of the 

Arithmetic composite and of the English composite as measures 

of these abilities in the grades studied. Applying the formula, 



n(n) 



, we get the following results: 



1 + (n - L)ri 

TABLE XII 
Approximate coefficient of 
reliabiUty of the Arithmetic 
composite as representa- 
tive of all the Arithmetic 
work of these grades 

.828 

.873 

.832 



Grad^ 



VI 

VII 

VIII 



Approximate coefficient of 
reUabifity of the Engfish 
composite as representative 
of all the English work of 
these grades 

.850 

.856 

.827 



Average . 844 . 844 

That is, on the basis of the correlation between the two Arith- 
metic composites the coefficient of rehability of the whole Arith- 
metic composite as a measure of the arithmetic work of these 
grades is .844, as an average for the three grades. It happens 
that the coefficient of reliability of the English composite is ex- 
actly the same. 



VI 



COMPARISON OF RESULTS IN OVERLAPPING WITH 
THOSE OF OTHER INVESTIGATORS 

So far as the writer is aware, no previous investigation has had 
as its special aim the study of overlapping. Many students of 
individual differences have reported overlapping figures on various 
bases, such as grade in school, age, sex, and race. Practically all 
the studies of achievements of school pupils, for whatever purpose, 
call attention to the overlapping of grades as a significant finding. 
It is the purpose of this chapter to report some of these results. 
In all cases where the data permit, per cents of overlapping have 
been calculated on the basis used in this study, where this had 
not already been done. Results for the sixth, seventh, and eighth 
grades only, where these grades are included in the data available, 
wiU be given, the purpose being to make as direct a comparison 
as possible. Some quotations will be made from these studies to 
show the nature of the conclusions based upon the extent of the 
overlapping. 

Chambers, in a study of "Individual Differences in Grammar 
Grade Children" (7), made in 1910, treats the question of over- 
lapping of grades at considerable length. He gave one test each 
in cancellation of A's, addition, spelling, association of opposites, 
auditory memory, and visual memory to 22 pupils in a seventh 
grade and the same number in an eighth grade. Relow are the 
per cents of overlapping calculated from his data. 



Per cents of overlapping 


Ca 


Ad 


Sp 


As 


Am 


Vm 


of Grade VII on Grade VIII.. 


..47 


43 


55 


55 


41 


52 



The author says on page 69, "Manifestly an extra year of school 
life has failed to produce any discernible improvement in the 

59 



60 The Overlapping of Attainments in Certain Grades 

traits tested. Indeed in two of the abilities concerning which the 
public is most insistent as to the school's responsibility, viz., ad- 
dition and spelling, the extra year in school seems to have pro- 
duced a positive deterioration: in addition the lowest rank is 
monopolized by a single eighth grade representative while the two 
highest ranks are preempted by two members of the seventh 
grade. In spelhng the lowest rank is occupied by four eighth 
and one seventh grade pupils, while the highest rank contains one 
from each grade." Further, on page 71: "The most important 
conclusion reached in the comparison of the distribution of abil- 
ities in the two grades is, then, that there is no line of demarca- 
tion between them; in regard to every trait examined the grades 
overlap and in regard to most traits they are coextensive in their 
range. Hence, to assume that in two school grades we have two 
distinct species, that certain abilities are lacking in one and present 
in the other, that all the members of one class are of approximately 
equal abiUty in a certain field and that they are all inferior in 
that ability to all the members of the other, is, at best, a very haz- 
ardous guess . . . Teachers cannot afford to forget that our 
school grades do not represent distinct gradations of ability in 
the pupils, but are simply convenient devices of administration to 
facilitate the handling of children in the mass. The grades are 
determined by reference to more or less artificial standards, and 
too often do not represent the real intelligence, industry, endur- 
ance, adaptability, and other traits important for education of 
the pupils. It seems as if ability in perception, association and 
memory, when these functions are tested on familiar material, 
should be pretty closely related to educability, and should be af- 
fected by school progress to an extent distinguishable in successive 
grades, if the grades really grade." 

Bonser (2) presents overlapping figures on the basis of both 
ages and grades, for each of seven tests of reasoning abifity of 
children in the fourth, fifth and sixth grades, and also for the 
combined results of the seven tests. Per cents of overlapping 
calculated from his data are given in Table XIII. 



Comparison of Results in Overlapping 61 

TABLE XIII 

Per Cent of Boys in One Grade Who Equal or Exceed the Median 
OF THE Other Grade 

Tests VB on VIB VA on VIA 

I and II— Arithmetic 25.46 32.31 

III— Controlled Association 35.95 30.43 

IV— Opposites 30.38 20.00 

V— Selective Judgment 33.23 19.23 

VI— Selective Judgment 21.84 30.77 

VII — Intellectual Interpretation of Poems 41.71 24.46 

Average 31 . 43 26 . 20 

Combined Results 23.54 7.69 

We have further evidence here of the high per cents of over- 
lapping by single tests and of the reduction of the overlapping by 
a composite of all the scores from that obtained by averaging the 
per cents for the different tests. Regarding the method of ob- 
taining the composite the author says on p. 72, "The sirnis of the 
results for the several tests have been taken and arrayed by the 
same distributions as the results .of each separate test." 

To compare further the overlapping figures by single tests and 
by composites Table XIV has been prepared by assembling the 
results for the different tests and for the composite as calculated 
by Bonser. 

TABLE XIV 

Per Cent of Boys in Each Grade Who Reach or Exceed the Ability 
Reached by the Highest 25 Per Cent of All the Boys Together 

Tests IVA VB VA VIB VIA 

landll 5.37 12.65 32.30 44.89 62.00 

III 17.20 22.77 27.68 42.85 52.00 

IV 7.52 18.97 24.56 42.85 54.00 

V 7.52 29.09 16.91 39.79 42.00 

VI 15.05 22.77 24.56 54.08 48.00 

VII 16.12 20.24 16.91 37.75 56.00 

Average 11.46 21.08 23.82 43.70 52.33 

Combined Results 9.67 18.97 19.95 42.85 62.00 

Here again we note a reduction of the figures for the lower 
grades in favor of the composites. It wiU be observed that in 



62 The Overlapping of Attainments in Certain Grades 

this table the higher figure for VIA, 62.00 for the composite as 
compared with the average, 52.33, argues in favor of the composite 
also, because the larger the per cent in the sixth grade the more 
superior is the sixth-grade attainment to that of the lower grades 
and hence the less the overlapping. 

Bonser gives the following as one of his "General Conclusions": 
"The point of greatest pragmatic significance for the school lies 
in the impUcations from the two facts, first, that there are quite 
substantial percentages from both the lower grade groups and 
lower age groups who are found in the highest quartile of ability 
for all; second, that most of the groups of the youngest 25 per cent 
in each grade show higher ability than the oldest 25 per cent and 
sometimes higher than that of the median abifity of the whole 
grade." (p. 91) 

Thorndike (18) in reporting Bonser's study makes the following 
comments. "It should be borne in mind, however, that (except 
with the 'opposite' test) the time allowed in each grade was not 
necessarily identical, each class being given such time as the 
quickest person in it required to complete the test. Bonser does 
not regard the time factor as of much consequence, in view of 
the nature of the tests, but it seems probable that the lower grades 
had longer time and so are credited with somewhat better relative 
scores than they would have obtained if all grades had been 
given in every test some constant time." (p. 64) After making 
these qualifications, Thorndike gives some striking interpretations 
of the overlapping figures. "If we drew at random 109 boys 
and girls from the 757 in all these grades to make up the VIA, 
this absolutely random drawing would differ from the IVA grade 
by half as much as does the group picked out administratively 
as two years in advance of it . . . Indeed I unhesitatingly 
assert that a month's test in respect to the ability to do the 
specific intellectual work of the school course of study would show 
a similar, though perhaps not so great, variability and a similar 
overlapping." (p. 66) 

Courtis (8) presents figures which show that 2.8 per cent 
of the fourth grade reach or exceed the median of the eighth, and 
4.1 per cent of the eighth go below the median of the fourth in 
the Courtis arithmetic tests. 

In his report of the use of the Courtis tests in the New York 
Inquiry (9) Courtis gives considerable space to the question of 



Comparison of Results in Overlapping 63 

overlapping. Typical results are as indicated below, calculated 
from data on page 441. 

28.9 per cent of the 6th grade reach or exceed the median of the 8th. 
40.6 per cent of the 6th grade reach or exceed the median of the 7th. 
36.1 per cent of the 7th grade reach or exceed the median of the 8th. 

Courtis makes the following comments: "So far as any in- 
dividual child is concerned, to say that he has completed the 
course in arithmetic in the pubHc schools is to convey no informa- 
tion as to his ability in even the simplest work." (p. 439) "The 
generaUzation to be made from this is that the amount of over- 
lapping of the grades is constant, and is, therefore, due to the one 
factor that is common to all the schools and grades— that is, to 
the inherent differences in children in their ability to respond to 
training in multiplication tables." (p. 450) 

The results obtained by Elliott (10) from single tests vary con- 
siderably among schools. He found that the per cents of over- 
lapping of all fifth grades on all seventh grades were as given 
below. 



School Systems 


Arithmetic 


Composition 


Spellkn 


A, B, C 


18.80 


4.50 


19.90 


D 


13.60 


17.30 


34.60 


E 


25.00 


0.00 


27.42 


F 


2.56 


4.87 


11.25 


G 


26.00 


55.10 


27.45 



Assembling Starch's figures as reported in Part I of the Fifteenth 
Yearbook of the National Society for the Study of Education (17), 
we get the following. 

Test Per Cent in any Grade Who Equal or Exceed 

THE Median of the Next Grade Above 
Reading 31 

Spelling 23 

Arithmetic 32 . 5 

With regard to a composite this author says, "A combined score 
for all studies was computed for each pupil so that the various 
subjects were balanced against each other. It was found that 
even then the overlapping was practically as large. Thirty-two 
and two-tenths per cent of the pupils in any given grade reach or 
exceed the standard of the next grade above it; thirty-five and 
two-tenths per cent fall to or below the standard of the next 



64 The Overlapping of Attainments in Certain Grades 

grade below." (p. 145) In the absence of distribution tables and 
any further statement of the method employed it is not possible 
to make any careful comparison with our figures. 

From a five-minute reading test, scored on the basis of repro- 
duction of matter read and answers to ten questions, Waldo (26) 
found that "many children in lower grades excel their school- 
mates in higher grades. Thus 29.5 per cent of the fifth graders 
excel the average rate in reading of the eighth grade; 36.1 per 
cent of them excel the seventh grade average, and 42.6 per cent 
excel the average for the sixth grade. 

"In reproduction there are smaller numbers of children who are 
superior to those of higher grades; but 16 children, or 26.2 per 
cent, excel the average of the sixth grade; and but 8, or 15.7 per 
cent, exceed the seventh grade average, and none are superior to 
the eighth." 

Thorndike (22) found that in handwriting "individual pupils 
within the same grade . . . show a range of difference much 
greater than that between the fifth grade of the worst system and 
the eighth grade of the best." 

Buckingham (5) reports results of tests given in New York 
City in 1915, as follows: 

Per Cent in Each Grade who Equal or Exceed 
THE Median of the Next Higher Grade 

Tests Vir on VIP VIP on VHP VHP on VHP 

Arithmetic 33 36 28 

Geography.... 47 39 28 

History 43 23 27 

Grammar ? 38 29 

Buckingham gave a test consisting of ten problems in arithme- 
tic to 4985 children in March and again a similar test in June, 
from the results of which he got per cents of overlapping as shown 
below (4). 

VH' VH^ VHi VH- VH^ VHP 

on on on on on on 

VH^ VIH^ VHP VHI^ VHP VHP 

March 37.3 25.3 11.3 36.2 19.9 30.0 

June 32.2 28.6 13.7 45.5 22.6 28.5 

Table XV brings together the results of a number of other 
studies. 



Comparison of Results in Overlapping 

TABLE XV 

SUMMARY OF RESULTS OF OTHER INVESTIGATIONS 

Peb Cent in Each Grade Who Equal or Exceed the Median of 
THE Other GitvDE 



65 







No. 


VI 


VI 


VII 


Investigators 


Tests 


of 
pupils 


on 
VIII 


on 
VII 


on 
VIII 


Buckingham (6) 


SpeUing 
100 words 


1060 


13.6 


34.0 


27.1 


Buckingham (6) 


Spelling 
100 words 


1940 


16.8 


36.1 


26.8 


Gray (11) 


Quality of 
Silent Reading 


1053 


28.8 


38.5 


38.4 


Trabue (25) 


Completion Test 
Scale A 


4337 


12.2 


25.4 


31.3 


Studebaker (19) 


Courtis 
Series B 












Addition 


2936 


31.4 


41.3 


38.7 




Subtraction- 


2930 


25.3 


40.8 


34.8 




Multiplication 


2941 


25.2 


42.8 


35.1 




Division 


2941 


21.2 


36.5 


30.3 


Salt Lake Survey (15) 


Stone 
Reasoning 


1161 


7.7 


25.7 


34.8 




Composition 


1667 


20.6 


38.9 


32.4 




Penmanship 


1736 


23.2 


30.2 


39.2 




Speed of Silent 


1165 


52.0 


43.7 


59.2 




Reading 










Kelly (13) 


Kansas Silent 
Reading 
2nd test 


3514 


27.4 


37.0 


42.2 


Butte Survey (14) 


Courtis Series B 414 
Multiplication 


10.5 


26.1 


26.4 




Stone 


416 


11.2 


24.2 


24.4 




Reasoning 











The one outstanding fact in all this is the great amount of over- 
lapping of grades when the pupils are tested with single or few tests. 
In the light of our discussion in Chapter IV, however, these large 



66 The Overlapping of Attainments in Certain Grades 

overlapping figures are not so disturbing as they might otherwise 
be. That many pupils in one grade excel the median pupil of a 
higher grade in a given test is not greatly significant, really telling 
us very little about the extent to which the grades overlap in abil- 
ity in a given trait. 

Overlapping of Attainments on the Age Basis 

While it is the purpose of this study to consider only the problem 
of overlapping of attainments in certain grades, it should be point- 
ed out that this represents only one basis for the study of over- 
lapping. Another very important question is the overlapping 
of the attainments of children of different age groups. Our 
data have not been treated in such a way as to show what the 
results from our testing would be. Table XVI has been prepared 
by bringing together figures in Bonser's study, in order to show 
the facts as he found them. The table is similar to Table XIV 
with the exception that here our basis is age rather than grade. 

TABLE XVI 

Per Cent of Boys in Each Age Group Who Reach the Ability Reached 
BY the Highest 25 Per Cent of All the Boys Together 

Age Groups 
Tests 8-11 11-12 12-13 13-16 

I and II 27.02 26.13 34.37 29.87 

III 27.92 39.60 22.90 35.04 

IV 29.72 32.67 27.06 19.47 

V 28.82 31.68 28.10 20.76 

VI 25.22 35.64 29.14 22.06 

VII 27.02 27.72 29.14 25.96 

Average 27.62 32.24 28.45 25.53 

Combined Results 26.12 29.70 21.86 23.36 

It is seen that roughly one-fourth of the boys in each of these 
four age groups reach the 75 percentile for the whole group. 
That is, the highest 25 per cent of the whole group is composed 
of about equal parts of each age group. Further it may be noted 
that the combined results are consistently lower than the averages 
of the single tests, and in one case, the 12-13 group, considerably 
lower. 



VII 
CONCLUSIONS 

1. This study supports the findings of other investigators in the 
generally high per cents of overlapping among the upper elemen- 
tary school grades when measured in terms of attainments in 
single tests. 

2. Recognising the limitations of such testing and letting the 
figures stand for just what they are, per cents of overlapping in 
the tests as given, we find that those tests which show the least 
amount of overlapping are, in order, Spelling, Problems I, Visual 
Vocabulary VIII, Visual Vocabulary XIII, Opposites A4, Op- 
posites A2, and Alpha 2. 

3. The large per cents of overlapping from single tests are ap- 
preciably reduced when the overlapping is based on the results 
from composites of two or more tests of a similar kind. 

4. There is still further reduction of the per cents of overlap- 
ping when these composites are further combined, so as to be more 
nearly representative of general ability to do the work of a given 
grade. 

5. It follows that the error in using overlapping figures from 
single tests as measures of the overlapping in a given trait is great. 
It is, of course, still greater if such figures are used as measures 
of general abiUty to do the work of the grade, even though a test 
be given in each study. 

6. Our grading system as a means of placing children accord- 
ing to abiUty to do the work of the school is not so grossly lacking 
as has been suggested on the basis of overlapping by single tests. 
On the other hand, our school grades do not represent distinct 
types of ability, so clearly marked off from each other that all 
the pupils of a given grade are superior to all the pupils of the 
next lower grade and inferior to all the pupils of the next higher 
grade in ability to do the work of the school. 

67 



68 The Overlapping of Attainments in Certain Grades 

7. The fact that the overlapping of Grades VII and VIII is in 
general higher than that of Grades VI and VII is further evidence 
in support of the belief that the eighth grade as at present main- 
tained in the ordinary eight grade scheme does not justify itself. 

8. Statements regarding the futility of a given half-year or 
year of school work are not sufficiently well founded on the basis 
of the large amount of overlapping of grades in certain tests. 

9. The arithmetic tests used in this study, treated by the com- 
posite method, have a high degree of rehability as a measure of 
the arithmetic work of these grades. The same is true of the 
Enghsh composite, the coefficient of reliability being .844 in each 
case, as an average for the three grades. 



VIII 
BIBLIOGRAPHY 

1. Ayres, Leonard P. Measuring Scale for Ability in Spelling. Russell 
Sage Foundation, New York City, Division of Education. 

2. BoNSER, Frederick G. The Reasoning Ability of Children of the 
Fourth, Fifth, and Sixth School Grades. Teachers College, Colum- 
bia University, Contributions to Education, No. 37. 

3. Brown, William. Essentials of Mental Measurement, p. 102. 

4. Buckingham, B. R. Notes on the Derivation of Scales in School 

Subjects. Fifteenth Yearbook of the National Society for the Study 
of Education, 1915, Part I, p. 33. 

5. Buckingham, B. R. Principles of Scale Derivation with Special Ap- 
plication to Arithmetic, Geography, History and Grammar. Third 
Annual Conference on Educational Measurements Bloomington, In- 
diana, 1916, p. 83. 

6. Buckingham, B. R. Spelling Ability: Its Measurement and Distribu- 
tion. Teachers College, Columbia University, Contributions to 
Education, No. 59, pp. 32, 68. 

7. Chambers, Will Grant. Individual Differences in Grammar Grade 
Children. Journal of Educational Psychology, Vol. 1, 1910, pp. 61-75. 

8. Courtis, S. A. Educational Diagnosis. Educational Administration 
and Supervision, Vol. 1, 1915, p. 93. 

9. Courtis, S. A. The Courtis Tests in Arithmetic. New York School 
Inquiry, Vol. I, pp. 391-546. 

10. Elliott, C. H. Variations in the Achievements of Pupils. Teach- 
ers College, Columbia University, Contributions to Education, No. 
72, p. 51. 

11. Gray, William Scott. Studies of Elementary School Reading 
through Standardized Tests. Supplementary Educational Mono- 
graphs, No. 1, University of Chicago Press, p. 116. 

69 



70 The Overlapping of Attainments in Certain Grades 

12. HoLLiNGWORTH, H. L. Correlation of Abilities as Affected by Prac- 

tice. Journal of Educational Psychology, Vol. 4, 1913, p. 411. 

13. Kelly, F. J. The Kansas Silent Reading Tests. Journal of Edu- 
cational Psychology, Vol. 7, 1916, p. 77. 

14. Report of A Survey of the School System of Butte, Montana, 1914. 

15. Report of a Survey of the School System of Salt Lake City, Utah, 1915. 

16. Starchj Daniel. Educational Measurements. 

17. Starch, Daniel. Standard Tests as Aids in the Classification and 

Promotion of Pupils. Fifteenth Yearbook of the National Society for 
the Study of Education, 1915, Part 1. 

18. Strayer and Thorndike. Educational Administration. 

19. Studebaker, J. W. Annual Report of the Des Moines Public Schools, 

1915, pp. 62-5. 

20. Thorndike, E. L. An Improved Scale for Measuring Ability in Read- 

ing. Teachers College Record, Vol. XVI: No. 5, Nov. 1915. 

21. Thorndike, E. L. Educational Psychology, Vol. Ill, pp. 177, 180-181. 

22. Thorndike, E. L. Handwriting. Teachers College Record, Vol. XI: 
No. 2, March 1910, p. 75. 

23. Thorndike, E. L. Preliminary Extension of the Hillegas Scale for 
the Measurement of Quality in EngUsh Composition by Young People. 
Teachers College, Columbia University. 

24. Thorndike, E. L. The Measurement of Ability in Reading. Teach- 
ers College Record, Vol. XV: No. 4, Sept. 1914. 

25. Trabue, M. R. Completion-Test Language Scales. Teachers 

College, Columbia University, Contributions to Education, No. 77. 

26. Waldo, Karl D. Tests in Reading in Sycamore Schools. Elemen- 
tary School Journal, Vol. 15, 1914-15, p. 261. 

27. Woody, Clifford. Measurements of Some Achievements in Arith- 

metic. Teachers College, Columbia University, Contributions to 
Education, No. 80. 



IX 

APPENDIX— DISTRIBUTIONS 

Ax)DiTioN Subtraction 

Grade Grade 

Score VI VII VIII Score VI VII VIII 



1 1 

2 2 

3 3 

4 4 

5 5 

6 6 

7 7 

8 8 

9 9 

10 10 

11 11 

12 12 

13 13 

14 14 

15 1 1 15 1 

16 1 16 

17 1 1 17 

18 3 . 18 

19 2 4 19 

20 2 4 20 

21 7 3 3 21 

22 4 7 6 22 

23 9 7 3 23 

24 10 10 24 

25 15 2 13 25 

26 12 23 2 26 

27 27 24 10 27 

28 23 18 1 28 

29 27 29 23 29 

30 16 20 21 10 

31 19 33 26 32 

32 20 17 27 33 

33 16 29 26 33 

34 15 14 27 34 

35 4 22 27 35 

36 5 17 22 

37 2 71 15 No. tested 238 302 267 

38 2 4 2 



1 


2 




1 


1 


1 


7 


1 


5 


6 


2 


1 


13 


16 


6 


17 


14 


7 


23 


12 


13 


28 


17 


8 


31 


16 


18 


24 


25 


19 


20 


31 


21 


16 


35 


43 


24 


36 


31 


9 


21 


39 


8 


27 


23 


6 


60 


14 


3 


14 


90 


1 


15 


17 
31 



Median Score 25 . 74 28 . 37 28 . 



No. tested 236 306 273 

Median Score 29.30 30.89 32.35 

71 



72 The Overlapping of Attainments in Certain Grades 









Distributions 










MULTIPUCATION 






Division 








Grade 








Grade 




Score 


VI 


VII 


VIII 


Score 


VI 


VII 


VII 




















1 








1 








2 








2 








3 








3 








4 








4 








5 








5 








6 








6 








7 








7 








8 








8 








9 








9 








10 








10 




1 




11 








11 








12 








12 


1 






13 








13 






1 


14 




1 




14 


3 


2 


2 


15 






1 


15 


6 


2 




16 




1 




16 


3 


5 




17 


3 


4 


2 


17 


4 


2 


1 


18 


5 


2 


1 


18 


14 


6 


7 


19 


4 


6 


1 


19 


11 


7 


8 


20 


3 


1 


1 


20 


15 


10 


3 


21 


7 


4 


5 


21 


13 


19 


12 


22 


11 


10 


6 


22 


14 


21 


11 


23 


8 


7 


4 


23 


18 


21 


17 


24 


21 


10 


10 


24 


28 


35 


20 


25 


11 


20 


17 


25 


20 


21 


21 


26 


27 


17 


11 


26 


21 


25 


39 


27 


22 


28 


16 


27 


24 


32 


32 


28 


20 


22 


17 


28 


16 


25 


24 


29 


25 


30 


23 


29 


8 


19 


23 


30 


21 


25 


31 


30 


10 


13 


19 


31 


19 


27 


22 


31 


2 


15 


13 


32 


16 


20 


25 


32 


1 


13 


11 


33 


3 


22 


37 


33 


2 


6 


4 


34 


1 


21 


16 


34 




3 


3 


35 


7 


12 


14 


35 




2 


1 


36 


3 


7 


6 


36 




2 




37 




5 


6 













38 




2 


1 


No. tested 


234 


307 


272 


39 




1 























Median Score 24.54 26.06 26.85 


No. tested 


237 


305 


273 











Median Score 27.84 29.65 30.69 



Appendix 



73 



Distributions 



Score 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

No. tested 



Problems I 

Grade 
VI VII 

16 3 

1 



236 



Median Score 9.11 



16 



VIII 



Score 


1 

2 
3 
4 
5 
6 
7 



Problems II 

Grade 
VI VII 



19 9 

2 10 

1 11 
21 12 

6 13 

3 14 

41 15 4 
2. 16 

2 17 

42 18 1 

2 

7 No. tested 239 305 
41 

3 Median Score 2.28 5.06 



1 
307 271 
15.36 18.35 



Problems III 



Score 

0- 2 
3- 5 
6- 8 
9-11 
12-14 
15-17 
18-20 



VI 

159 
40 
30 



107 
66 
73 

24 

28 

10 

2 



VIII 

23 

10 

19 

37 

12 

9 

49 

8 

7 

46 

2 

2 

32 

1 
13 



3 

273 
6.54 



VII VIII 



No. tested 240 310 
Median Score ... 5.18 



41 

52 
59 
50 
39 
28 
4 

273 

3.21 



The Overlapping of Attainments in Certain Grades 



Distributions 




Trabue-B 


Trabue-C 


Grade 


Grade 


VI VII VIII 


VI VII 



Score VI VII VIII VI VII VIII 








1 




2 




3 




4 


1 


5 




6 


1 


7 




8 


4 


9 


5 


10 


23 


II 


19 


12 


50 


13 


51 


14 


44 


15 


16 


16 


12 


17 


14 


18 


4 


19 




20 




No. tested 


244 


Median Score 


13.37 



1 

3 1 

6 2 

5 2 

17 7 
27 14 

38 38 
49 46 

39 44 
47 38 
44 28 

18 26 
5 16 
2 1 
1 7 

302 270 

14.13 14.57 



1 






4 


3 


I 


5 


5 




12 


14 


4 


9 


24 


10 


40 


34 


23 


53 


44 


33 


44 


48 


35 


34 


40 


47 


17 


38 


34 


18 


27 


40 


2 


10 


18 


4 


15 


17 




1 


8 
3 


244 


303 


273 


12.94 


13.57 


14.65 



Appendix 75 



DiSTMBUTTONS 

Tbabue-D Trabue-E 

Grade Grade 

Score VI VII VIII VI VII VIII 

1 
2 
3 
4 
5 
6 

7 2 

8 1 6 3 

9 6 3 3 

10 10 9 4 

11 15 14 9 

12 43 35 28 

13 32 45 27' 

14 68 64 49 

15 34 45 39 

16 27 44 49 

17 4 25 36 

18 3 9 15 

19 3 6 

20 3 

No. tested 245 302 271 

Median Score 14.20 14.61 15.32 





1 




7 


2 


1 


4 


9 


7 


18 


16 


4 


27 


22 


10 


50 


44 


22 


51 


62 


31 


38 


49 


39 


28 


39 


42 


15 


32 


47 


3 


11 


21 


2 


9 


31 




2 


8 




5 


7 


243 


303 


270 


13.30 


13.93 


15.50 



76 The Overlapping of Attainments in Certain Grades 





DiSTRreUTIONS 








Reading-Alpha 2 








Grade 




Score 


VI 


VII 


VIII 











1 








2 








3 








4 








5 








6 








7 








8 








9 


1 






10 








11 


1 


1 


1 


12 


2 




13 


4 


1 




14 


2 


3 




15 
16 


5 
8 


3 
1 


3 


17 


8 


7 




18 


14 


10 


3 


19 


23 


9 


6 


20 


18 


14 


5 


21 


27 


21 


5 


22 


18 


19 


19 


23 


22 


26 


14 


24 


17 


27 


26 


25 


23 


33 


21 


26 


25 


32 


30 


27 


15 


31 


38 


28 
29 
30 
31 
32 


6 

7 
1 
1 


34 
11 
12 
11 

1 


43 

27 

15 

13 

3 


33 




1 




34 








35 








36 








37 








38 









No. tested 


248 


308 


272 


Median Score 


22.61 


25.37 


27. 0{ 



Appendix 77 

Distributions 
OpposiTEs-Al Opposites-A2 

Grade Grade 

Score VI VII VIII VI VII VIII 



5 11 1 

10 111 

15 1 1 

20 11 4 1 

25 4 4 

30 15 7 

35 2 16 9 3 

40 19 9 5 

45 1 33 18 14 

50 29 22 21 

55 1 1 32 28 23 

60 1 1 31 42 25 

65 26 27 23 

70 1 - 9 30 32 

75 3 8 34 27 

80 1 3 24 22 

85 2 1 5 22 32 

90 13 1 11 15 

95 5 5 1 2 6 14 

100 5 5 1 2 11 

105 10 5 2 4 1 

110 13 11 5 11 

115 36 26 18 2 

120 80 72 43 1 

125 61 84 81 1 

130 20 67 77 

135 6 22 41 

No. tested 248 306 276 249 310 274 

Median Score 122.69 126.19 128.77 53.71 66.11 73.44 



78 The Overlapping of Attainments in Certain Grades 







DiSTMBUTIONS 










Opposites-A3 




OPPOSITES-A4 






Grade 






Grade 




Score 


VI 


VII 


VIII 


VI 


VII 


VIII 





7 


4 




5 


4 




5 


2 


2 


1 


3 


1 




10 


2 


2 




6 


4 


2 


15 


7 


1 




10 


3 




20 


9 


4 


2 


10 


4 


2 


25 


9 


6 




17 


9 


2 


30 


17 


11 


7 


19 


7 


6 


35 


25 


10 


9 


20 


15 


2 


40 


28 


26 


7 


21 


21 


10 


45 


21 


37 


14 


21 


27 


9 


50 


36 


38 


24 


17 


27 


14 


55 


25 


35 


27 


27 


20 


22 


60 


17 


31 


32 


19 


15 


23 


65 


19 


16 


22 


20 


33 


28 


70 


8 


16 


20 


16 


37 


23 


75 


6 


19 


30 


9 


25 


25 


80 


6 


16 


21 


6 


14 


29 


85 


3 


9 


22 


1 


22 


19 


90 


1 


5 


11 


1 


4 


15 


95 


1 


3 


13 


2 


7 


14 


100 


1 


10 


9 




8 


13 


105 




2 


1 


1 


6 


5 


110 






1 




1 


5 


115 










1 


2 


120 












1 


125 














130 














135 















No. tested 250 303 273 251 315 271 

Median Score 49.52 56.50 68.07 48.45 65.08 73.37 



Appendix 79 





Distributions 


le-Paj 


IT-Bl 

Grade 




VI 


VII 


VIII 


3 


1 


6 


7 


12 


11 


11 


14 


10 


16 


4 


10 


10 


10 


10 


4 


7 


6 


4 


5 


8 


4 


7 


7 


2 


7 


5 


8 


5 


7 


10 


4 


3 


6 


4 


4 


8 


6 


4. 


2 


7 


4 


9 


5 


10 


15 


11 


6 


15 


13 


17 


18 


26 


15 


22 


31 


33 


41 


56 


47 


38 


79 


50 



Adjective-Substajvtive-B2 



Score 



1 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 



No. tested 253 314 273 249 314 273 

Median Score 16.50 18.29 17.57 





Grade 




VI 


VII 


VII 


18 


12 


9 


13 


11 


5 


3 


6 


1 


3 


1 


3 


1 


2 


2 


1 


1 


2 


2 


1 




1 






1 




2 
1 


2 


1 




1 


1 




2 


1 


1 


4 


1 


2 


2 


2 


1 


3 


1 


2 


9 


10 


11 


11 


14 


11 


38 


48 


38 


134 


201 


182 



80 



The Overlapping of Attainments in Certain Grades 



Distributions 

Verb-Object-C 1 

Grade 
VI VII VIII 



Species-Ge]vus-C2 



Score 


1 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 



No. tested 242 312 

Median Score 29.28 29.62 







1 






1 




3 






2 




2 


1 




5 


3 
1 




2 


4 


1 


3 


2 


3 


7 


6 


1 


8 


7 


3 


15 


14 


11 


13 


25 


18 


37 


31 


22 


71 


82 


66 


70 


25 


145 



VI 



Grade 
VII 



VIII 



273 



1 






3 






1 


3 




3 


2 


1 


2 


4 


2 


4 




1 


5 


4 


2 


4 


4 


1 


4 


4 




3 


2 


2 


3 


4 


2 


3 


5 


3 


2 


3 


4 


3 


3 


5 


2 


1 


1 


1 


4 


4 


4 


5 




3 


4 


3 


5 


1 


5 


9 


5 


6 


4 


11 


4 


8 


14 


6 


18 


5 


8 


19 


15 


12 


24 


36 


12 


26 


32 


34 


39 


51 


57 


30 


50 


62 


9 


40 


35 


243 


312 


273 


26.27 


27.56 


28.31 



Appendix 81 









Distributions 




Spelling 








Grade 




jcore 


VI 


VII 


VIII 





1 


1 




1 


6 






2 


4 


3 




3 


8 


5 




4 


7 


4 




5 


10 


4 


1 


6 


11 


6 




7 


11 


6 


1 


8 


20 


2 


4 


9 


13 


8 


1 


10 


17 


11 


3 


11 


10 


10 


5 


12 


11 


10 


7 


13 


11 


12 


^ 


14 


19 


21 


7 


15 


16 


20 


12 


16 


21 


24 


20 


17 


19 


33 


31 


18 


19 


33 


39 


19 


8 


44 


61 


20 


10 


47 


74 



No. tested 252 304 272 

Median Score 12.73 17.15 18.97 



Part-Whole-C3 




Grade 




VI 


VII 

1 


VIII 


1 


1 
3 




2 


9 


3 


4 


1 


2 


6 


3 


1 


2 


5 


2 


8 


8 


5 


5 


5 


9 


15 


10 


10 


11 


17 


4 


19 


21 


13 


17 


22 


11 


20 


24 


31 


29 


35 


22 


24 


51 


39 


29 


34 


46 


26 


26 


34 


15 


27 


27 


7 


7 


18 


240 


310 


274 


15.34 


15.71 


16.69 



82 The Overlapping of Attainments in Certain Grades 



Distributions 
Mixed Relations-D1 Mixed Relations-D2 







Grade 






Grade 




Score 


VI 


VII 


VIII 


VI 


VII 


VII] 





2 


5 


3 


2 


3 




2 


3 


2 


2 


1 


4 


1 


4 


6 


1 


2 


1 


2 


4 


6 


7 


11 


6 


11 


9 


6 


8 


11 


20 


13 


12 


21 


5 


10 


14 


24 


20 


23 


39 


11 


12 


31 


43 


33 


34 


36 


18 


14 


48 


56 


38 


26 


26 


34 


16 


51 


29 


16 


26 


22 


26 


18 


22 


30 


22 


11 


17 


22 


20 


14 


19 


9 


6 


9 


8 


22 


11 


10 


5 


6 


6 


12 


24 


7 


7 


7 


4 


14 


6 


26 


5 


7 


10 


■ 7 


13 


11 


28 


4 


7 


5 


10 


5 


7 


30 


6 


14 


10 


20 


10 


8 


32 


3 


6 


13 


20 


16 


18 


34 


3 


11 


14 


19 


19 


19 


36 


2 


5 


7 


8 


30 


34 


38 




2 


8 


2 


10 


22 


40 




2 




2 


1 


1 



No. tested 250 311 273 251 312 273 

Median Score 16.12 15.76 16.85 17.19 17.45 22.25 



Appendix 83 





Distributions 


DiRECTIONS-X 






Grade 




VI 


VII 


VIII 


1 






1 






1 


1 
1 
3 


1 


3 


4 




2 


2 


2 


5 


2 


5 


6 


5 


3 


12 


4 


6 


13 


11 


12 


30 


18 


25 


16 


14 


16 


48 


50 


46 


13 


29 


13 


66 


99 


91 


5 


7 


8 


24 


57 


50 



DiRECTIONS-VII 

Grade 
Score VI VII VIII VI VII VIII 



1 1 1 

2 11 1 
3 
4 
5 
6 
7 



No. tested 246 307 278 247 309 277 

Median Score 14.69 16.10 16.11 10.17 10.59 11.33 



3 


3 


2 


12 


9 


6 


31 


24 


17 


62 


67 


34 


74 


82 


72 


29 


38 


45 


20 


41 


46 


7 


16 


21 


5 


16 


17 




2 


4 


1 


8 


7 



84 The Overlapping of Attainments in Certain Grades 









DlSTRIBlITIONS 










DiRECTIONS-VI 








Composition 








Grade 










Grade 




Score 


VI 


VII 


VIII 




Score 


VI 


VII 


VIII 






















1 










5 








2 










10 








3 










15 


2 


2 




4 










20 




2 




5 










25 


24 


5 




6 










30 


60 


35 


11 


7 










35 


77 


65 


22 


8 










40 


35 


84 


47 


9 










45 


25 


54 


72 


10 










50 


22 


41 


63 


11 










55 


8 


22 


47 


12 










60 


1 


3 


13 


13 










65 




1 


7 


14 


1 








70 




1 


1 


15 


2 


1 






75 








16 


1 


8 


2 




80 








17 


11 


13 


6 




85 








18 


49 


36 


34 




90 








19 


138 


175 


177 




95 








20 


45 


76 


58 


























No. 


tested 


254 


315 


283 


1. tested 


247 


309 


277 













Median Score 19.43 19.55 19. 55. Median Score 37.66 42.89 49.27 



Appendix 



85 



Distributions 
Visual Vocabulary-VIII Visual VocABtriARy — ^XIII 







Grade 








Grade 




Score 


VI 


VII 


VIII 


Score 


VI 


VII 


VII] 









1 





1 






5 




1 




10 


9 


4 


1 


10 


1 






20 


21 


8 


1 


15 








30 


18 


8 


2 


20 






1 


40 


12 


17 


4 


25 


1 


2 


1 


50 


21 


17 


12 


30 


5 


1 




60 


28 


17 


11 


35 


2 


2 




70 


26 


28 


13 


40 


2 


1 


2 


80 


23 


22 


15 


45 


8 


2 




90 


22 


31 


17 


50 


14 


7 


2 


100 


19 


32 


33 


55 


19 


19 


I 


110 


22 


34 


31 


60 


35 


23 


7 


120 


19 


36 


45 


65 


36 


17 


10- 


130 


4 


31 


47 


70 


42 


43 


16 


140 


3 


19 


31 


75 


37 


58 


40 


150 




3 


12 


80 


21 


62 


61 


160 






1 


85 


23 


35 


85 


170 




1 




90 


2 


23 


31 













95 




11 


18 


No. tested 


248 


308 


276 


100 




1 




Median Score 


75.38 


100.63 


119.35 



No. tested 248 308 276 

Median Score 70 .12 78 . 10 84 . 67 



86 



The Overlapping of Attainments in Certain Grades 



Distributions 
Opposites Composite Controlled Association Composite 

A2-A3-A4 B1-B2-C1-C2-C3 







Grade 








Grade 




Score 


VI 


VII 


VIII 


Score 


VI 


VII 


VIII 





3 


2 













10 


1 






5 






1 


20 


1 


2 




10 








30 


2 


3 




15 


1 






40 


2 


1 


1 


20 








50 


5 






25 


2 






60 


6 


1 


1 


30 








70 


8 


3 




35 


1 






80 


4 


4 


1 


40 


2 


2 




90 


6 


5 


2 


45 


2 


2 




100 


14 


5 


2 


50 


1 


3 


2 


110 


20 


5 


1 


55 


3 


4 




120 


16 


17 


4 


60 


4 


7 




130 


12 


11 


10 


65 


13 


4 


2 


140 


18 


18 


12 


70 


11 


8 


8 


150 


26 


20 


11 


75 


9 


7 


6 


160 


21 


20 


7 


80 


1.5 


17 


14 


170 


13 


24 


19 


85 


20 


16 


12 


180 


19 


23 


21 


90 


18 


15 


25 


190 


16 


18 


13 


95 


20 


39 


24 


200 


12 


20 


24 


100 


29 


30 


22 


210 


6 


21 


18 


105 


37 


38 


37 


220 


6 


17 


23 


110 


40 


68 


58 


230 




18 


19 


115 


24 


50 


57 


240 




12 


14 


120 




2 


3 


250 




7 


17 












260 




7 


13 


No. tested 


250 


312 


271 


270 




2 


14 










280 




4 


8 


Median Score 


100.86 


107.63 


107.64 


290 




4 


7 










300 


1 


7 


4 










310 




3 


2 










320 






3 










330 






2 










340 






1 











No. tested 249 304 274 

Median Score 152.50 184.78 214.44 



Appendix 



87 









Distributions 








Mixed Relations Composite 


Directions 


Composite 


Score 


D1-D2 

Grade 
VI VII 


VIII 


Score 


X-VI-VII 

Grade 
VI VII 


VII 







2 













4 


2 






2 








8 


2 


3 




4 








12 


2 


7 


4 


6 








16 


13 


12 


13 


8 








20 


20 


36 


11 


10 








24 


30 


47 


27 


12 








28 


42 


40 


44 


14 








32 


30 


24 


26 


16 








36 


22 


26 


28 


18 








40 


19 


20 


14 


20 








44 


16 


18 


12 


22 








48 


14 


7 


14 


24 




2 




52 


11 


14 


12 


26 


3 






56 


10 


12 


-9 


28 


1 






60 


3 


6 


10 


30 




3 




64 


7 


12 


15 


32 


1 


3 


4 


68 


3 


14 


17 


34 


7 


3 


3 


72 


3 


8 


14 


36 


9 


14 


11 


76 


1 


4 


6 


38 


32 


13 


14 


80 








40 


36 


26 


28 


No. tested 


250 


312 


276 


42 
44 


53 
53 


53 
73 


34 
63 


Median Score 


33.86 


33.40 


37.86 


46 
48 


37 
12 


66 
29 


67 
32 










50 


3 


20 


18 










52 




3 


3 










54 
















56 









No. tested 247 308 277 

Median Score 43.30 45.01 45.41 



88 



The Overlapping of Attainments in Certain Grades 









Distributions 








Visual Vocabulary Composite 


Trabue Composite 






VIII-XIII 








B-C-D-E 








Grade 










Grade 




Score 


VI 


VII 


VIII 




Score 



VI 


VII 


VIII 













5 








10 










10 








20 




1 






15 








30 


1 








20 








40 






1 




25 


1 






50 


3 








30 


1 






60 


7 


3 






35 


8 


8 




70 


10 


4 






40 


15 


23 


6 


80 


10 


4 


1 




45 


61 


47 


31 


90 


12 


11 


1 




50 


80 


77 


51 


100 


14 


7 


4 




55 


59 


80 


70 


110 


17 


15 


6 




60 


13 


46 


65 


120 


22 


9 


9 




65 


4 


23 


33 


130 


13 


18 


6 




70 




1 


12 


140 


27 


19 


6 




75 






4 


150 


27 


19 


16 




80 








160 


17 


23 


7 















170 


14 


24 


21 


No. 


tested 


242 


305 


272 


180 


15 


28 


32 












190 


17 


34 


25 


Median Score 


52.19 


54.84 


58.43 


200 


13 


24 


31 












210 


5 


27 


35 












220 


3 


21 


38 












230 


1 


11 


22 












240 




4 


9 












250 




2 


6 












260 



















No. tested 248 308 276 

Median Score 145.56 178.75 200.97 



Appendix 89 

Distributions 
Abithmetic Composite — Addition, Subtraction, Multiplication, 



Division, 


Problems I, 


Problems II 






Grade 




Score 


VI 


VII 


VIII 


70 




1 


1 


75 


3 


2 




80 


4 


3 




85 


9 


4 


1 


90 


11 


6 


5 


95 


14 


7 


3 


100 


18 


8 


6 


105 


28 


8 


6 


110 


23 


23 


8 


115 


24 


34 


8 


120 


31 


21 


23 


125 


25 


29 


23 


130 


17 


28 


20 


135 


'13 


26 


26 


140 


5 


25 


33 


145 


6 


18 


30 


150 


3 


29 


27 


155 


1 


13 


20 


160 


2 


5 


13 


165 


1 


10 


13 


170 




6 


6 


175 




2 


3 


180 








185 








190 








195 









No. tested 238 308 275 

Median 116.88 131.43 141.14 



90 The Overlapping of Attainments in Certain Grades 

Distributions 

English Composite 

Grade Including all of the tests or groups 

Score VI VII VIII of tests in the Total Composite ex- 

190 1 cept Arithmetic 

200 1 

210 2 

220 1 

230 2 

240 6 1 

250 4 4 

260 6 1 

270 8 4 2 

280 9 3 

290 8 6 2 

300 20 10 1 

310 16 7 4 

320 12 18 2 

330 23 15 12 

340 22 28 9 

350 24 21 8 

360 18 27 17 

370 19 26 15 

380 21 22 28 

390 11 23 17 

400 5 21 23 

410 8 20 34 

420 5 13 17 

430 3 13 17 

440 1 17 19 

450 1 10 20 

460 3 14 

470 2 11 

480 4 2 

490 1 3 

500 1 3 

510 2 

No. tested 255 323 282 

Median Score 344.77 375.58 410 29 



Appendix 91 



Distributions 
Total Composite 
Grade 
Score VI VII VIII Including: 



360 




1 




380 
400 


2 
4 


1 




420 


5 


1 




440 


6 


4 


1 


460 


7 


2 


1 


480 


19 


11 


1 


500 


16 


10 


4 


520 


26 


6 


6 


540 


23 


18 


3 


560 


17 


17 


7 


580 


32 


32 


9 


600 


29 


27 


16 


620 


20 


35 


22 


640 


19 


33 


29 


660 


13 


25 


27 


680 


9 


23 


31 


700 


3 


22 


29 


720 


2 


18 


22- 


740 


2 


24 


31 


760 




5 


16 


780 




4 


16 


800 




2 


9 


820 




3 


2 



Arithmetic Composite 

Trabue Composite 

Alpha 2 

Spelling 

Composition 

Opposites Composite 

Controlled Association (B-C) 

Composite 
Mixed Relations Composite 
Directions Composite 
Visual Vocabulary Composite 



No. tested 254 324 282 

Median Score 581.35 638 28 689.68 

Per Cents of Overlapping for Tests Not Included in Table II 

VI VI VII VIII VIII VII 

on on on on on on 

Tests VIII VII VIII VI VII VI 

Al 16.53 25.19 35.84 20.70 34.88 32.59 

Bl 42.98 37.40 56.42 40.11 55.89 36.78 

B2 

CI 27.19 40.07 37.66 29.48 37.70 41.01 

C2 23.01 36.81 40.13 27.96 38.11 36.13 

X 35.67 35.93 49.55 36.60 49.68 32.41 

VI 43.36 43.36 50.08 42.64 50.31 43.12 

PHI 7.87 21.63 26 84 ... 28.86 



